diff --git a/bin/build_variables.sh b/bin/build_variables.sh
index bbed2572..cf7bb143 100644
--- a/bin/build_variables.sh
+++ b/bin/build_variables.sh
@@ -21,4 +21,4 @@ MPIRVER=3.0.0 # MPIR build no longer works (not clear where to download from)
 # These are the actual dependencies used (at least by default):
 GMPVER=6.3.0
 MPFRVER=4.2.2
-FLINTVER='3.3.1'
+FLINTVER=3.4.0
diff --git a/meson.build b/meson.build
index 16860da3..8c96b6e5 100644
--- a/meson.build
+++ b/meson.build
@@ -13,7 +13,7 @@ project(
 # then we can consider not using a speculative upper version cap here.
 #
 flint_lower = '>=3.0'
-flint_upper = '<3.4'
+flint_upper = '<3.5'
 cython_lower = '>=3.0.11'
 cython_upper = '<3.3'