diff --git a/Sofa/Component/Mass/src/sofa/component/mass/NodalMassDensity.cpp b/Sofa/Component/Mass/src/sofa/component/mass/NodalMassDensity.cpp
index cb5f531971c..5697e159e75 100644
--- a/Sofa/Component/Mass/src/sofa/component/mass/NodalMassDensity.cpp
+++ b/Sofa/Component/Mass/src/sofa/component/mass/NodalMassDensity.cpp
@@ -25,12 +25,14 @@
 namespace sofa::component::mass
 {
 
-template class SOFA_COMPONENT_MASS_API NodalMassDensity<SReal>;
+template class SOFA_COMPONENT_MASS_API NodalMassDensity<double>;
+template class SOFA_COMPONENT_MASS_API NodalMassDensity<float>;
 
 void registerNodalMassDensity(sofa::core::ObjectFactory* factory)
 {
     factory->registerObjects(core::ObjectRegistrationData("Definition of a nodal mass density (one value per dof).")
-        .add< NodalMassDensity<SReal> >()
+        .add< NodalMassDensity<double> >()
+        .add< NodalMassDensity<float> >()
     );
 }
 
diff --git a/applications/plugins/SofaCUDA/Component/CMakeLists.txt b/applications/plugins/SofaCUDA/Component/CMakeLists.txt
index effab0275a9..e30a18bc29d 100644
--- a/applications/plugins/SofaCUDA/Component/CMakeLists.txt
+++ b/applications/plugins/SofaCUDA/Component/CMakeLists.txt
@@ -36,7 +36,8 @@ set(HEADER_FILES
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaMeshMatrixMass.inl
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaUniformMass.h
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaUniformMass.inl
-    
+    ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaFEMMass.h
+
 
     ### solidmechanics
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/solidmechanics/fem/elastic/CudaFEMKernelUtils.cuh
@@ -114,6 +115,7 @@ set(SOURCE_FILES
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaDiagonalMass.cpp
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaMeshMatrixMass.cpp
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaUniformMass.cpp
+    ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/mass/CudaFEMMass.cpp
 
     ### Solidmechanics
     ${SOFACUDA_COMPONENT_SOURCE_DIR}/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cpp
diff --git a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/init.cpp b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/init.cpp
index 968cd603fb6..794b720ae7f 100644
--- a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/init.cpp
+++ b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/init.cpp
@@ -81,6 +81,7 @@ extern void registerRigidMapping(sofa::core::ObjectFactory* factory);
 extern void registerDiagonalMass(sofa::core::ObjectFactory* factory);
 extern void registerMeshMatrixMass(sofa::core::ObjectFactory* factory);
 extern void registerUniformMass(sofa::core::ObjectFactory* factory);
+extern void registerFEMMass(sofa::core::ObjectFactory* factory);
 
 // component::mechanicalload
 extern void registerConstantForceField(sofa::core::ObjectFactory* factory);
@@ -221,6 +222,7 @@ void registerObjects(sofa::core::ObjectFactory* factory)
     registerDiagonalMass(factory);
     registerMeshMatrixMass(factory);
     registerUniformMass(factory);
+    registerFEMMass(factory);
     registerConstantForceField(factory);
     registerEllipsoidForceField(factory);
     registerLinearForceField(factory);
diff --git a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/mass/CudaFEMMass.cpp b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/mass/CudaFEMMass.cpp
new file mode 100644
index 00000000000..71487b3f72d
--- /dev/null
+++ b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/mass/CudaFEMMass.cpp
@@ -0,0 +1,85 @@
+/******************************************************************************
+*                 SOFA, Simulation Open-Framework Architecture                *
+*                    (c) 2006 INRIA, USTL, UJF, CNRS, MGH                     *
+*                                                                             *
+* This program is free software; you can redistribute it and/or modify it     *
+* under the terms of the GNU Lesser General Public License as published by    *
+* the Free Software Foundation; either version 2.1 of the License, or (at     *
+* your option) any later version.                                             *
+*                                                                             *
+* This program is distributed in the hope that it will be useful, but WITHOUT *
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or       *
+* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
+* for more details.                                                           *
+*                                                                             *
+* You should have received a copy of the GNU Lesser General Public License    *
+* along with this program. If not, see <http://www.gnu.org/licenses/>.        *
+*******************************************************************************
+* Authors: The SOFA Team and external contributors (see Authors.txt)          *
+*                                                                             *
+* Contact information: contact@sofa-framework.org                             *
+******************************************************************************/
+#define SOFA_GPU_CUDA_CUDAFEMMASS_CPP
+
+#include <SofaCUDA/component/config.h>
+
+#include <sofa/gpu/cuda/CudaTypes.h>
+#include <SofaCUDA/component/mass/CudaFEMMass.h>
+#include <sofa/component/mass/FEMMass.inl>
+#include <sofa/core/behavior/Mass.inl>
+#include <sofa/core/ObjectFactory.h>
+#include <sofa/fem/FiniteElement[all].h>
+
+namespace sofa::component::mass
+{
+
+using namespace sofa::gpu::cuda;
+
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3fTypes, sofa::geometry::Edge>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3fTypes, sofa::geometry::Triangle>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3fTypes, sofa::geometry::Quad>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3fTypes, sofa::geometry::Tetrahedron>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3fTypes, sofa::geometry::Hexahedron>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3fTypes, sofa::geometry::Prism>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3fTypes, sofa::geometry::Pyramid>;
+
+#ifdef SOFA_GPU_CUDA_DOUBLE
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3dTypes, sofa::geometry::Edge>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3dTypes, sofa::geometry::Triangle>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3dTypes, sofa::geometry::Quad>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3dTypes, sofa::geometry::Tetrahedron>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3dTypes, sofa::geometry::Hexahedron>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3dTypes, sofa::geometry::Prism>;
+template class SOFACUDA_COMPONENT_API FEMMass<CudaVec3dTypes, sofa::geometry::Pyramid>;
+#endif
+
+} // namespace sofa::component::mass
+
+namespace sofa::gpu::cuda
+{
+
+void registerFEMMass(sofa::core::ObjectFactory* factory)
+{
+    using namespace sofa::component::mass;
+
+    factory->registerObjects(sofa::core::ObjectRegistrationData("Supports GPU-side computations using CUDA for FEMMass")
+        .add< FEMMass<CudaVec3fTypes, sofa::geometry::Edge> >()
+        .add< FEMMass<CudaVec3fTypes, sofa::geometry::Triangle> >()
+        .add< FEMMass<CudaVec3fTypes, sofa::geometry::Quad> >()
+        .add< FEMMass<CudaVec3fTypes, sofa::geometry::Tetrahedron> >()
+        .add< FEMMass<CudaVec3fTypes, sofa::geometry::Hexahedron> >()
+        .add< FEMMass<CudaVec3fTypes, sofa::geometry::Prism> >()
+        .add< FEMMass<CudaVec3fTypes, sofa::geometry::Pyramid> >()
+#ifdef SOFA_GPU_CUDA_DOUBLE
+        .add< FEMMass<CudaVec3dTypes, sofa::geometry::Edge> >()
+        .add< FEMMass<CudaVec3dTypes, sofa::geometry::Triangle> >()
+        .add< FEMMass<CudaVec3dTypes, sofa::geometry::Quad> >()
+        .add< FEMMass<CudaVec3dTypes, sofa::geometry::Tetrahedron> >()
+        .add< FEMMass<CudaVec3dTypes, sofa::geometry::Hexahedron> >()
+        .add< FEMMass<CudaVec3dTypes, sofa::geometry::Prism> >()
+        .add< FEMMass<CudaVec3dTypes, sofa::geometry::Pyramid> >()
+#endif
+    );
+}
+
+} // namespace sofa::gpu::cuda
diff --git a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/mass/CudaFEMMass.h b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/mass/CudaFEMMass.h
new file mode 100644
index 00000000000..bb847a6f167
--- /dev/null
+++ b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/mass/CudaFEMMass.h
@@ -0,0 +1,52 @@
+/******************************************************************************
+*                 SOFA, Simulation Open-Framework Architecture                *
+*                    (c) 2006 INRIA, USTL, UJF, CNRS, MGH                     *
+*                                                                             *
+* This program is free software; you can redistribute it and/or modify it     *
+* under the terms of the GNU Lesser General Public License as published by    *
+* the Free Software Foundation; either version 2.1 of the License, or (at     *
+* your option) any later version.                                             *
+*                                                                             *
+* This program is distributed in the hope that it will be useful, but WITHOUT *
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or       *
+* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
+* for more details.                                                           *
+*                                                                             *
+* You should have received a copy of the GNU Lesser General Public License    *
+* along with this program. If not, see <http://www.gnu.org/licenses/>.        *
+*******************************************************************************
+* Authors: The SOFA Team and external contributors (see Authors.txt)          *
+*                                                                             *
+* Contact information: contact@sofa-framework.org                             *
+******************************************************************************/
+#pragma once
+
+#include <SofaCUDA/component/config.h>
+
+#include <sofa/gpu/cuda/CudaTypes.h>
+#include <sofa/component/mass/FEMMass.h>
+
+namespace sofa::component::mass
+{
+
+#ifndef SOFA_GPU_CUDA_CUDAFEMMASS_CPP
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3fTypes, sofa::geometry::Edge>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3fTypes, sofa::geometry::Triangle>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3fTypes, sofa::geometry::Quad>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3fTypes, sofa::geometry::Tetrahedron>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3fTypes, sofa::geometry::Hexahedron>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3fTypes, sofa::geometry::Prism>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3fTypes, sofa::geometry::Pyramid>;
+
+#ifdef SOFA_GPU_CUDA_DOUBLE
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3dTypes, sofa::geometry::Edge>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3dTypes, sofa::geometry::Triangle>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3dTypes, sofa::geometry::Quad>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3dTypes, sofa::geometry::Tetrahedron>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3dTypes, sofa::geometry::Hexahedron>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3dTypes, sofa::geometry::Prism>;
+extern template class SOFACUDA_COMPONENT_API FEMMass<sofa::gpu::cuda::CudaVec3dTypes, sofa::geometry::Pyramid>;
+#endif
+#endif
+
+} // namespace sofa::component::mass
diff --git a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cpp b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cpp
index ca58990357d..ce190709333 100644
--- a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cpp
+++ b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cpp
@@ -35,6 +35,8 @@ template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3fTyp
 template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Quad>;
 template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Tetrahedron>;
 template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Hexahedron>;
+template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Prism>;
+template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Pyramid>;
 
 #ifdef SOFA_GPU_CUDA_DOUBLE
 template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Edge>;
@@ -42,6 +44,8 @@ template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3dTyp
 template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Quad>;
 template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Tetrahedron>;
 template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Hexahedron>;
+template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Prism>;
+template class SOFACUDA_COMPONENT_API CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Pyramid>;
 #endif
 
 } // namespace sofa::component::solidmechanics::fem::elastic
@@ -54,48 +58,24 @@ void registerCorotationalFEMForceField(sofa::core::ObjectFactory* factory)
     using namespace sofa::component::solidmechanics::fem::elastic;
 
     factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for EdgeCorotationalFEMForceField")
+        "Supports GPU-side computations using CUDA for CorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Edge> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for TriangleCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Triangle> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for QuadCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Quad> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for TetrahedronCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Tetrahedron> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for HexahedronCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Hexahedron> >()
-    );
-
+        .add< CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Prism> >()
+        .add< CudaCorotationalFEMForceField<CudaVec3fTypes, sofa::geometry::Pyramid> >()
 #ifdef SOFA_GPU_CUDA_DOUBLE
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for EdgeCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Edge> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for TriangleCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Triangle> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for QuadCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Quad> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for TetrahedronCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Tetrahedron> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for HexahedronCorotationalFEMForceField")
         .add< CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Hexahedron> >()
-    );
+        .add< CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Prism> >()
+        .add< CudaCorotationalFEMForceField<CudaVec3dTypes, sofa::geometry::Pyramid> >()
 #endif
+    );
 }
 
 } // namespace sofa::gpu::cuda
diff --git a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cu b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cu
index a34a75c7646..3b0a486ecc1 100644
--- a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cu
+++ b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaCorotationalFEMForceField.cu
@@ -315,17 +315,25 @@ void CorotationalFEMForceFieldCuda_addDForce(
 INSTANTIATE_COROTATIONAL(float, 2)
 INSTANTIATE_COROTATIONAL(float, 3)
 INSTANTIATE_COROTATIONAL(float, 4)
+INSTANTIATE_COROTATIONAL(float, 5) // Pyramid
+INSTANTIATE_COROTATIONAL(float, 6) // Prism
 INSTANTIATE_COROTATIONAL(float, 8)
 INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(float, 3)
 INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(float, 4)
+INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(float, 5) // Pyramid
+INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(float, 6) // Prism
 INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(float, 8)
 
 INSTANTIATE_COROTATIONAL(double, 2)
 INSTANTIATE_COROTATIONAL(double, 3)
 INSTANTIATE_COROTATIONAL(double, 4)
+INSTANTIATE_COROTATIONAL(double, 5) // Pyramid
+INSTANTIATE_COROTATIONAL(double, 6) // Prism
 INSTANTIATE_COROTATIONAL(double, 8)
 INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(double, 3)
 INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(double, 4)
+INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(double, 5) // Pyramid
+INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(double, 6) // Prism
 INSTANTIATE_COROTATIONAL_WITH_ROTATIONS(double, 8)
 
 #undef INSTANTIATE_COROTATIONAL
diff --git a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cpp b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cpp
index 0c624c5b03e..83c0c67d5e5 100644
--- a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cpp
+++ b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cpp
@@ -35,6 +35,8 @@ template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec
 template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Quad>;
 template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Tetrahedron>;
 template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Hexahedron>;
+template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Prism>;
+template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Pyramid>;
 
 #ifdef SOFA_GPU_CUDA_DOUBLE
 template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Edge>;
@@ -42,6 +44,8 @@ template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec
 template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Quad>;
 template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Tetrahedron>;
 template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Hexahedron>;
+template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Prism>;
+template class SOFACUDA_COMPONENT_API CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Pyramid>;
 #endif
 
 } // namespace sofa::component::solidmechanics::fem::elastic
@@ -54,48 +58,24 @@ void registerLinearSmallStrainFEMForceField(sofa::core::ObjectFactory* factory)
     using namespace sofa::component::solidmechanics::fem::elastic;
 
     factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for EdgeLinearSmallStrainFEMForceField")
+        "Supports GPU-side computations using CUDA for LinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Edge> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for TriangleLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Triangle> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for QuadLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Quad> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for TetrahedronLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Tetrahedron> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA for HexahedronLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Hexahedron> >()
-    );
-
+        .add< CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Prism> >()
+        .add< CudaLinearSmallStrainFEMForceField<CudaVec3fTypes, sofa::geometry::Pyramid> >()
 #ifdef SOFA_GPU_CUDA_DOUBLE
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for EdgeLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Edge> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for TriangleLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Triangle> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for QuadLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Quad> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for TetrahedronLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Tetrahedron> >()
-    );
-    factory->registerObjects(sofa::core::ObjectRegistrationData(
-        "Supports GPU-side computations using CUDA (double) for HexahedronLinearSmallStrainFEMForceField")
         .add< CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Hexahedron> >()
-    );
+        .add< CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Prism> >()
+        .add< CudaLinearSmallStrainFEMForceField<CudaVec3dTypes, sofa::geometry::Pyramid> >()
 #endif
+    );
 }
 
 } // namespace sofa::gpu::cuda
diff --git a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cu b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cu
index e625c701d49..c4d645838e5 100644
--- a/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cu
+++ b/applications/plugins/SofaCUDA/Component/src/SofaCUDA/component/solidmechanics/fem/elastic/CudaLinearSmallStrainFEMForceField.cu
@@ -177,11 +177,15 @@ void LinearSmallStrainFEMForceFieldCuda_addDForce(
 INSTANTIATE_LINEAR(float, 2)
 INSTANTIATE_LINEAR(float, 3)
 INSTANTIATE_LINEAR(float, 4)
+INSTANTIATE_LINEAR(float, 5) // Pyramid
+INSTANTIATE_LINEAR(float, 6) // Prism
 INSTANTIATE_LINEAR(float, 8)
 
 INSTANTIATE_LINEAR(double, 2)
 INSTANTIATE_LINEAR(double, 3)
 INSTANTIATE_LINEAR(double, 4)
+INSTANTIATE_LINEAR(double, 5) // Pyramid
+INSTANTIATE_LINEAR(double, 6) // Prism
 INSTANTIATE_LINEAR(double, 8)
 
 #undef INSTANTIATE_LINEAR
diff --git a/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaCorotationalFEMForceField_prism.scn b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaCorotationalFEMForceField_prism.scn
new file mode 100644
index 00000000000..0d6c13dad2e
--- /dev/null
+++ b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaCorotationalFEMForceField_prism.scn
@@ -0,0 +1,43 @@
+<?xml version="1.0" ?>
+<Node name="root" gravity="0 -9.81 0" dt="0.01">
+    <RequiredPlugin pluginName="Sofa.Component.Constraint.Projective"/>
+    <RequiredPlugin pluginName="Sofa.Component.Engine.Select"/>
+    <RequiredPlugin pluginName="Sofa.Component.LinearSolver.Iterative"/>
+    <RequiredPlugin pluginName="Sofa.Component.Mass"/>
+    <RequiredPlugin pluginName="Sofa.Component.ODESolver.Backward"/>
+    <RequiredPlugin pluginName="Sofa.Component.SolidMechanics.FEM.Elastic"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Container.Constant"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Container.Grid"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Mapping"/>
+    <RequiredPlugin pluginName="Sofa.Component.Visual"/>
+    <RequiredPlugin pluginName="SofaCUDA"/>
+
+    <VisualStyle displayFlags="showBehaviorModels showForceFields" />
+    <DefaultAnimationLoop />
+    <DefaultVisualManagerLoop />
+
+    <Node name="Prism">
+        <Node name="Beam">
+            <RegularGridTopology name="grid" n="40 10 10" min="0 6 -2" max="16 10 2" />
+        </Node>
+
+        <Node name="Simulated">
+            <EulerImplicitSolver name="cg_odesolver" rayleighStiffness="0.1" rayleighMass="0.1" />
+            <CGLinearSolver iterations="20" name="linear solver" tolerance="1.0e-12" threshold="1.0e-12" />
+
+            <MechanicalObject position="@../Beam/grid.position" name="Volume" template="CudaVec3f"/>
+
+            <MeshTopology name="Container" />
+            <Hexa2PrismTopologicalMapping input="@../Beam/grid" output="@Container" />
+
+            <NodalMassDensity property="0.2"/>
+            <FEMMass template="CudaVec3f,Prism"/>
+            <BoxROI name="ROI1" box="-0.1 5 -3 0.1 11 3" drawBoxes="1" />
+
+            <FixedProjectiveConstraint indices="@ROI1.indices" />
+            <CudaCorotationalFEMForceField name="FEM" template="CudaVec3f,Prism"
+                                           youngModulus="2000" poissonRatio="0.3"/>
+        </Node>
+    </Node>
+
+</Node>
diff --git a/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaCorotationalFEMForceField_pyramid.scn b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaCorotationalFEMForceField_pyramid.scn
new file mode 100644
index 00000000000..7733aa92c89
--- /dev/null
+++ b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaCorotationalFEMForceField_pyramid.scn
@@ -0,0 +1,50 @@
+<?xml version="1.0" ?>
+<Node name="root" gravity="0 -9.81 0" dt="0.01">
+    <RequiredPlugin pluginName="Sofa.Component.Constraint.Projective"/>
+    <RequiredPlugin pluginName="Sofa.Component.LinearSolver.Iterative"/>
+    <RequiredPlugin pluginName="Sofa.Component.Mass"/>
+    <RequiredPlugin pluginName="Sofa.Component.ODESolver.Backward"/>
+    <RequiredPlugin pluginName="Sofa.Component.SolidMechanics.FEM.Elastic"/>
+    <RequiredPlugin pluginName="Sofa.Component.StateContainer"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Container.Constant"/>
+    <RequiredPlugin pluginName="Sofa.Component.Visual"/>
+    <RequiredPlugin pluginName="SofaCUDA"/>
+
+    <VisualStyle displayFlags="showBehaviorModels showForceFields" />
+    <DefaultAnimationLoop />
+    <DefaultVisualManagerLoop />
+
+    <Node name="Pyramid">
+        <EulerImplicitSolver name="cg_odesolver" rayleighStiffness="0.1" rayleighMass="0.1" />
+        <CGLinearSolver iterations="20" name="linear solver" tolerance="1.0e-12" threshold="1.0e-12" />
+
+        <!-- A cube made of 6 pyramids -->
+        <MeshTopology name="Container" pyramids="
+            0 1 5 4 8
+            1 5 6 2 8
+            2 3 7 6 8
+            0 3 7 4 8
+            3 2 1 0 8
+            6 7 4 5 8
+        "
+        position="
+            -1 -1 -1
+            1 -1 -1
+            1 1 -1
+            -1 1 -1
+            -1 -1 1
+            1 -1 1
+            1 1 1
+            -1 1 1
+            0 0 0
+        "/>
+        <MechanicalObject template="CudaVec3f" name="Volume" />
+
+        <NodalMassDensity property="10"/>
+        <FEMMass template="CudaVec3f,Pyramid"/>
+        <FixedProjectiveConstraint indices="2 3 7 6"/>
+        <CudaCorotationalFEMForceField name="FEM" template="CudaVec3f,Pyramid"
+                                       youngModulus="500" poissonRatio="0.45"/>
+    </Node>
+
+</Node>
diff --git a/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaLinearSmallStrainFEMForceField_prism.scn b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaLinearSmallStrainFEMForceField_prism.scn
new file mode 100644
index 00000000000..e7e30a3f603
--- /dev/null
+++ b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaLinearSmallStrainFEMForceField_prism.scn
@@ -0,0 +1,43 @@
+<?xml version="1.0" ?>
+<Node name="root" gravity="0 -9.81 0" dt="0.01">
+    <RequiredPlugin pluginName="Sofa.Component.Constraint.Projective"/>
+    <RequiredPlugin pluginName="Sofa.Component.Engine.Select"/>
+    <RequiredPlugin pluginName="Sofa.Component.LinearSolver.Iterative"/>
+    <RequiredPlugin pluginName="Sofa.Component.Mass"/>
+    <RequiredPlugin pluginName="Sofa.Component.ODESolver.Backward"/>
+    <RequiredPlugin pluginName="Sofa.Component.SolidMechanics.FEM.Elastic"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Container.Constant"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Container.Grid"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Mapping"/>
+    <RequiredPlugin pluginName="Sofa.Component.Visual"/>
+    <RequiredPlugin pluginName="SofaCUDA"/>
+
+    <VisualStyle displayFlags="showBehaviorModels showForceFields" />
+    <DefaultAnimationLoop />
+    <DefaultVisualManagerLoop />
+
+    <Node name="Prism">
+        <Node name="Beam">
+            <RegularGridTopology name="grid" n="40 10 10" min="0 6 -2" max="16 10 2" />
+        </Node>
+
+        <Node name="Simulated">
+            <EulerImplicitSolver name="cg_odesolver" rayleighStiffness="0.1" rayleighMass="0.1" />
+            <CGLinearSolver iterations="20" name="linear solver" tolerance="1.0e-12" threshold="1.0e-12" />
+
+            <MechanicalObject position="@../Beam/grid.position" name="Volume" template="CudaVec3f"/>
+
+            <MeshTopology name="Container" />
+            <Hexa2PrismTopologicalMapping input="@../Beam/grid" output="@Container" />
+
+            <NodalMassDensity property="0.2"/>
+            <FEMMass template="CudaVec3f,Prism"/>
+            <BoxROI name="ROI1" box="-0.1 5 -3 0.1 11 3" drawBoxes="1" />
+
+            <FixedProjectiveConstraint indices="@ROI1.indices" />
+            <CudaLinearSmallStrainFEMForceField name="FEM" template="CudaVec3f,Prism"
+                                                youngModulus="2000" poissonRatio="0.3"/>
+        </Node>
+    </Node>
+
+</Node>
diff --git a/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaLinearSmallStrainFEMForceField_pyramid.scn b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaLinearSmallStrainFEMForceField_pyramid.scn
new file mode 100644
index 00000000000..85b53b7e588
--- /dev/null
+++ b/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/CudaLinearSmallStrainFEMForceField_pyramid.scn
@@ -0,0 +1,50 @@
+<?xml version="1.0" ?>
+<Node name="root" gravity="0 -9.81 0" dt="0.01">
+    <RequiredPlugin pluginName="Sofa.Component.Constraint.Projective"/>
+    <RequiredPlugin pluginName="Sofa.Component.LinearSolver.Iterative"/>
+    <RequiredPlugin pluginName="Sofa.Component.Mass"/>
+    <RequiredPlugin pluginName="Sofa.Component.ODESolver.Backward"/>
+    <RequiredPlugin pluginName="Sofa.Component.SolidMechanics.FEM.Elastic"/>
+    <RequiredPlugin pluginName="Sofa.Component.StateContainer"/>
+    <RequiredPlugin pluginName="Sofa.Component.Topology.Container.Constant"/>
+    <RequiredPlugin pluginName="Sofa.Component.Visual"/>
+    <RequiredPlugin pluginName="SofaCUDA"/>
+
+    <VisualStyle displayFlags="showBehaviorModels showForceFields" />
+    <DefaultAnimationLoop />
+    <DefaultVisualManagerLoop />
+
+    <Node name="Pyramid">
+        <EulerImplicitSolver name="cg_odesolver" rayleighStiffness="0.1" rayleighMass="0.1" />
+        <CGLinearSolver iterations="20" name="linear solver" tolerance="1.0e-12" threshold="1.0e-12" />
+
+        <!-- A cube made of 6 pyramids -->
+        <MeshTopology name="Container" pyramids="
+            0 1 5 4 8
+            1 5 6 2 8
+            2 3 7 6 8
+            0 3 7 4 8
+            3 2 1 0 8
+            6 7 4 5 8
+        "
+        position="
+            -1 -1 -1
+            1 -1 -1
+            1 1 -1
+            -1 1 -1
+            -1 -1 1
+            1 -1 1
+            1 1 1
+            -1 1 1
+            0 0 0
+        "/>
+        <MechanicalObject template="CudaVec3f" name="Volume" />
+
+        <NodalMassDensity property="10"/>
+        <FEMMass template="CudaVec3f,Pyramid"/>
+        <FixedProjectiveConstraint indices="2 3 7 6"/>
+        <CudaLinearSmallStrainFEMForceField name="FEM" template="CudaVec3f,Pyramid"
+                                            youngModulus="500" poissonRatio="0.45"/>
+    </Node>
+
+</Node>