diff --git a/lib/elixir/lib/module/types/apply.ex b/lib/elixir/lib/module/types/apply.ex
index 3170cb96ff..37d4cdee14 100644
--- a/lib/elixir/lib/module/types/apply.ex
+++ b/lib/elixir/lib/module/types/apply.ex
@@ -447,6 +447,9 @@ defmodule Module.Types.Apply do
       :badtuple ->
         remote_error(:erlang, :element, [integer(), tuple_type], expr, stack, context)
 
+      :badindex when index < 1 ->
+        remote_error({:negindex, index - 1}, :erlang, :element, 2, expr, stack, context)
+
       :badindex ->
         remote_error({:badindex, index, tuple_type}, :erlang, :element, 2, expr, stack, context)
     end
@@ -473,12 +476,39 @@ defmodule Module.Types.Apply do
         args_types = [integer(), tuple_type, elem_type]
         remote_error(:erlang, :insert_element, args_types, expr, stack, context)
 
+      :badindex when index < 1 ->
+        remote_error({:negindex, index - 1}, :erlang, :insert_element, 3, expr, stack, context)
+
       :badindex ->
         error = {:badindex, index - 1, tuple_type}
         remote_error(error, :erlang, :insert_element, 3, expr, stack, context)
     end
   end
 
+  defp do_remote(:erlang, :setelement, [index, tuple, elem], _, expr, stack, context, of_fun)
+       when is_integer(index) do
+    tuple_type = open_tuple(List.duplicate(term(), max(index, 1)))
+
+    {tuple_type, context} = of_fun.(tuple, tuple_type, expr, stack, context)
+    {elem_type, context} = of_fun.(elem, term(), expr, stack, context)
+
+    case tuple_replace_at(tuple_type, index - 1, elem_type) do
+      value_type when is_descr(value_type) ->
+        {return(value_type, [tuple_type, elem_type], stack), context}
+
+      :badtuple ->
+        args_types = [integer(), tuple_type, elem_type]
+        remote_error(:erlang, :setelement, args_types, expr, stack, context)
+
+      :badindex when index < 1 ->
+        remote_error({:negindex, index - 1}, :erlang, :setelement, 3, expr, stack, context)
+
+      :badindex ->
+        error = {:badindex, index, tuple_type}
+        remote_error(error, :erlang, :setelement, 3, expr, stack, context)
+    end
+  end
+
   defp do_remote(:erlang, :delete_element, [index, tuple], _, expr, stack, context, of_fun)
        when is_integer(index) do
     tuple_type = open_tuple(List.duplicate(term(), max(index, 1)))
@@ -491,6 +521,9 @@ defmodule Module.Types.Apply do
       :badtuple ->
         remote_error(:erlang, :delete_element, [integer(), tuple_type], expr, stack, context)
 
+      :badindex when index < 1 ->
+        remote_error({:negindex, index - 1}, :erlang, :delete_element, 2, expr, stack, context)
+
       :badindex ->
         error = {:badindex, index, tuple_type}
         remote_error(error, :erlang, :delete_element, 2, expr, stack, context)
@@ -1808,6 +1841,29 @@ defmodule Module.Types.Apply do
     }
   end
 
+  def format_diagnostic({{:negindex, index}, mfac, expr, context}) do
+    traces = collect_traces(expr, context)
+    {mod, fun, arity, _converter} = mfac
+    mfa = Exception.format_mfa(mod, fun, arity)
+
+    %{
+      details: %{typing_traces: traces},
+      message:
+        IO.iodata_to_binary([
+          """
+          expected a non-negative integer as index in #{mfa}:
+
+              #{expr_to_string(expr) |> indent(4)}
+
+          got the index:
+
+              #{index}
+          """,
+          format_traces(traces)
+        ])
+    }
+  end
+
   def format_diagnostic({{:badkeydomain, map, key, error}, mfac, expr, context}) do
     {mod, fun, arity, _converter} = mfac
     mfa = Exception.format_mfa(mod, fun, arity)
diff --git a/lib/elixir/lib/module/types/descr.ex b/lib/elixir/lib/module/types/descr.ex
index bbef71f22a..ae368b238b 100644
--- a/lib/elixir/lib/module/types/descr.ex
+++ b/lib/elixir/lib/module/types/descr.ex
@@ -5850,8 +5850,16 @@ defmodule Module.Types.Descr do
 
   def tuple_insert_at(descr, index, type) when is_integer(index) and index >= 0 do
     case :maps.take(:dynamic, unfold(type)) do
-      :error -> tuple_insert_at_checked(descr, index, type)
-      {dynamic, _static} -> dynamic(tuple_insert_at_checked(descr, index, dynamic))
+      :error ->
+        tuple_insert_at_checked(descr, index, type)
+
+      {dynamic_type, _static} ->
+        # Errors about the tuple/index do not become "dynamic errors" when the
+        # inserted value happens to be dynamic — propagate them as-is.
+        case tuple_insert_at_checked(descr, index, dynamic_type) do
+          atom when atom in [:badtuple, :badindex] -> atom
+          result -> dynamic(result)
+        end
     end
   end
 
@@ -5919,6 +5927,97 @@ defmodule Module.Types.Descr do
     end)
   end
 
+  @doc """
+  Replace an element in the tuple at the given (0-based) index.
+
+  It returns the same as `tuple_fetch/2`.
+  """
+  def tuple_replace_at(:term, _key, _type), do: :badtuple
+
+  def tuple_replace_at(descr, index, type) when is_integer(index) and index >= 0 do
+    case :maps.take(:dynamic, unfold(type)) do
+      :error ->
+        tuple_replace_at_checked(descr, index, type)
+
+      {dynamic_type, _static} ->
+        # Errors about the tuple/index do not become "dynamic errors" when the
+        # replacement value happens to be dynamic — propagate them as-is.
+        case tuple_replace_at_checked(descr, index, dynamic_type) do
+          atom when atom in [:badtuple, :badindex] -> atom
+          result -> dynamic(result)
+        end
+    end
+  end
+
+  def tuple_replace_at(_, _, _), do: :badindex
+
+  defp tuple_replace_at_checked(descr, index, type) do
+    case :maps.take(:dynamic, descr) do
+      :error ->
+        # Note: the empty type is not a valid input
+        is_proper_tuple? = descr_key?(descr, :tuple) and non_empty_tuple_only?(descr)
+        is_proper_size? = tuple_of_size_at_least_static?(descr, index + 1)
+
+        cond do
+          is_proper_tuple? and is_proper_size? -> tuple_replace_static(descr, index, type)
+          is_proper_tuple? -> :badindex
+          true -> :badtuple
+        end
+
+      {dynamic, static} ->
+        is_proper_tuple? = descr_key?(dynamic, :tuple) and tuple_only?(static)
+        is_proper_size? = tuple_of_size_at_least_static?(static, index + 1)
+
+        cond do
+          is_proper_tuple? and is_proper_size? ->
+            static_result = tuple_replace_static(static, index, type)
+
+            # Prune for dynamic values that make the operation succeed.
+            dynamic_input = intersection(dynamic, tuple_of_size_at_least(index + 1))
+
+            if empty?(dynamic_input) and empty?(static) do
+              :badindex
+            else
+              dynamic_result = tuple_replace_static(dynamic_input, index, type)
+              union(dynamic(dynamic_result), static_result)
+            end
+
+          # Highlight the case where the issue is an index out of range from the tuple
+          is_proper_tuple? ->
+            :badindex
+
+          true ->
+            :badtuple
+        end
+    end
+  end
+
+  defp tuple_replace_static(descr, _, _) when descr == @none, do: none()
+
+  defp tuple_replace_static(descr, index, type) do
+    # Unlike insert/delete, replace is not injective at the replaced index, so
+    # transformed negative leaves would discard valid outputs. We eliminate
+    # negations first by converting to a positive-only DNF and replacing in
+    # each disjunct.
+    Map.update!(descr, :tuple, fn bdd ->
+      tuple_bdd_to_dnf_no_negations(bdd)
+      |> Enum.reduce(:bdd_bot, fn {tag, elements}, acc ->
+        # If the tuple is open, then we want List.replace_at to update the correct
+        # index, which requires filling the tuple with `term()` values first.
+        # Closed tuples of an incorrect size will have been cancelled by the
+        # earlier intersection with `tuple_of_size_at_least`.
+        elements =
+          if tag == :open and length(elements) < index + 1 do
+            tuple_fill(elements, index + 1)
+          else
+            elements
+          end
+
+        bdd_union(acc, tuple_new(tag, List.replace_at(elements, index, type)))
+      end)
+    end)
+  end
+
   defp tuple_of_size_at_least(n) when is_integer(n) and n >= 0 do
     %{tuple: tuple_new(:open, List.duplicate(term(), n))}
   end
diff --git a/lib/elixir/test/elixir/module/types/descr_test.exs b/lib/elixir/test/elixir/module/types/descr_test.exs
index 53c49536b7..5e72142ca3 100644
--- a/lib/elixir/test/elixir/module/types/descr_test.exs
+++ b/lib/elixir/test/elixir/module/types/descr_test.exs
@@ -1808,6 +1808,25 @@ defmodule Module.Types.DescrTest do
       assert dynamic(union(tuple(), integer()))
              |> tuple_delete_at(1)
              |> equal?(dynamic(tuple_of_size_at_least(1)))
+
+      # Deleting beyond a dynamic fixed-size tuple must fail with :badindex.
+      # In particular, deleting index N from a dynamic N-tuple must NOT
+      # silently return the original tuple type (off-by-one pruning bug).
+      assert tuple_delete_at(dynamic(tuple([atom([:ok]), term()])), 2) == :badindex
+      assert tuple_delete_at(dynamic(tuple([atom([:a]), atom([:b])])), 2) == :badindex
+      assert tuple_delete_at(dynamic(tuple([atom([:ok])])), 1) == :badindex
+
+      # Deletion is not injective at the deleted position; the negative
+      # constraint at that position must not be preserved.
+      assert difference(tuple([atom(), atom()]), tuple([atom([:a]), term()]))
+             |> tuple_delete_at(0)
+             |> equal?(tuple([atom()]))
+
+      # Negative constraints at positions OTHER than the deleted one are
+      # preserved (after shifting).
+      assert difference(tuple([atom(), atom()]), tuple([atom([:a]), term()]))
+             |> tuple_delete_at(1)
+             |> equal?(difference(tuple([atom()]), tuple([atom([:a])])))
     end
 
     test "tuple_insert_at" do
@@ -1881,6 +1900,126 @@ defmodule Module.Types.DescrTest do
       assert dynamic(union(tuple(), integer()))
              |> tuple_insert_at(1, boolean())
              |> equal?(dynamic(open_tuple([term(), boolean()])))
+
+      # Errors must propagate even when the inserted value is dynamic
+      assert tuple_insert_at(integer(), 0, dynamic()) == :badtuple
+      assert tuple_insert_at(term(), 0, dynamic()) == :badtuple
+      assert tuple_insert_at(tuple([atom([:ok])]), 2, dynamic()) == :badindex
+      assert tuple_insert_at(tuple([atom([:ok])]), -1, dynamic()) == :badindex
+
+      # Out-of-bounds insertions into a dynamic fixed-size tuple must fail
+      # with :badindex (rather than silently producing dynamic(none())).
+      assert tuple_insert_at(dynamic(tuple([atom([:ok]), term()])), 3, binary()) ==
+               :badindex
+
+      assert tuple_insert_at(dynamic(tuple([atom([:ok])])), 2, binary()) == :badindex
+
+      # Even at index 0 (where the size constraint is vacuous) the dynamic
+      # upper bound must still be intersected with the tuple domain so that
+      # non-tuple alternatives are pruned. `Tuple.insert_at/3` always returns
+      # a tuple, so an integer alternative cannot survive the operation.
+      assert tuple_insert_at(dynamic(term()), 0, boolean()) ==
+               dynamic(open_tuple([boolean()]))
+
+      assert tuple_insert_at(dynamic(union(tuple(), integer())), 0, boolean()) ==
+               dynamic(open_tuple([boolean()]))
+    end
+
+    test "tuple_replace_at" do
+      assert tuple_replace_at(tuple([integer(), atom()]), 2, boolean()) == :badindex
+      assert tuple_replace_at(tuple([integer(), atom()]), -1, boolean()) == :badindex
+      assert tuple_replace_at(empty_tuple(), 0, boolean()) == :badindex
+      assert tuple_replace_at(integer(), 0, boolean()) == :badtuple
+      assert tuple_replace_at(term(), 0, boolean()) == :badtuple
+      assert tuple_replace_at(tuple([none()]), 0, boolean()) == :badtuple
+
+      # Out-of-bounds in a union
+      assert union(tuple([integer(), atom()]), tuple([float()]))
+             |> tuple_replace_at(1, boolean()) == :badindex
+
+      # Test replacing an element in a closed tuple
+      assert tuple_replace_at(tuple([integer(), atom(), boolean()]), 1, float()) ==
+               tuple([integer(), float(), boolean()])
+
+      # Test replacing the first element of a closed tuple
+      assert tuple_replace_at(tuple([integer(), atom()]), 0, boolean()) ==
+               tuple([boolean(), atom()])
+
+      # Test replacing the last element of a closed tuple
+      assert tuple_replace_at(tuple([integer(), atom()]), 1, boolean()) ==
+               tuple([integer(), boolean()])
+
+      # Test replacing in an open tuple
+      assert tuple_replace_at(open_tuple([integer(), atom(), boolean()]), 1, float()) ==
+               open_tuple([integer(), float(), boolean()])
+
+      # Test replacing with a dynamic type
+      assert tuple_replace_at(tuple([integer(), atom()]), 1, dynamic()) ==
+               dynamic(tuple([integer(), term()]))
+
+      # Test replacing in a dynamic tuple
+      assert tuple_replace_at(dynamic(tuple([integer(), atom()])), 1, boolean()) ==
+               dynamic(tuple([integer(), boolean()]))
+
+      # Test replacing in a union of tuples
+      assert tuple_replace_at(union(tuple([integer()]), tuple([atom()])), 0, boolean()) ==
+               tuple([boolean()])
+
+      # Test replacing in an intersection of tuples
+      assert intersection(tuple([integer(), atom()]), tuple([term(), boolean()]))
+             |> tuple_replace_at(1, float()) == tuple([integer(), float()])
+
+      # Test replacing in a difference of tuples
+      assert difference(tuple([integer(), atom(), boolean()]), tuple([term(), term()]))
+             |> tuple_replace_at(1, float())
+             |> equal?(tuple([integer(), float(), boolean()]))
+
+      # Replacing in a difference where the negation actually constrains the
+      # positive (not just by arity). The replaced position drops its negative
+      # constraint, the other positions keep theirs.
+      assert difference(tuple([atom(), atom()]), tuple([atom([:a]), term()]))
+             |> tuple_replace_at(0, boolean())
+             |> equal?(tuple([boolean(), atom()]))
+
+      assert difference(tuple([atom(), atom()]), tuple([atom([:a]), term()]))
+             |> tuple_replace_at(1, boolean())
+             |> equal?(difference(tuple([atom(), boolean()]), tuple([atom([:a]), boolean()])))
+
+      # Errors must propagate even when the replacement value is dynamic
+      assert tuple_replace_at(integer(), 0, dynamic()) == :badtuple
+      assert tuple_replace_at(term(), 0, dynamic()) == :badtuple
+      assert tuple_replace_at(tuple([atom([:ok])]), 1, dynamic()) == :badindex
+      assert tuple_replace_at(empty_tuple(), 0, dynamic()) == :badindex
+
+      # Out-of-bounds writes to a dynamic fixed-size tuple must fail with :badindex
+      assert tuple_replace_at(dynamic(tuple([atom([:ok]), term()])), 2, binary()) ==
+               :badindex
+
+      assert tuple_replace_at(dynamic(tuple([atom([:ok])])), 1, binary()) == :badindex
+
+      # Test replacing in a complex union involving dynamic
+      assert union(tuple([integer(), atom()]), dynamic(tuple([float(), binary()])))
+             |> tuple_replace_at(1, boolean())
+             |> equal?(
+               union(
+                 tuple([integer(), boolean()]),
+                 dynamic(tuple([float(), boolean()]))
+               )
+             )
+
+      # Successfully replacing at position `index` in a tuple means that the dynamic
+      # values that succeed are intersected with tuples of size at least `index + 1`
+      assert dynamic(tuple())
+             |> tuple_replace_at(0, boolean())
+             |> equal?(dynamic(open_tuple([boolean()])))
+
+      assert dynamic(term())
+             |> tuple_replace_at(0, boolean())
+             |> equal?(dynamic(open_tuple([boolean()])))
+
+      assert dynamic(union(tuple(), integer()))
+             |> tuple_replace_at(1, boolean())
+             |> equal?(dynamic(open_tuple([term(), boolean()])))
     end
 
     test "tuple_values" do
diff --git a/lib/elixir/test/elixir/module/types/expr_test.exs b/lib/elixir/test/elixir/module/types/expr_test.exs
index dc6831f1b5..224eb865eb 100644
--- a/lib/elixir/test/elixir/module/types/expr_test.exs
+++ b/lib/elixir/test/elixir/module/types/expr_test.exs
@@ -813,6 +813,17 @@ defmodule Module.Types.ExprTest do
 
                    {:ok, integer()}
                """
+
+      assert typeerror!(elem({1, 2}, -1)) ==
+               ~l"""
+               expected a non-negative integer as index in Kernel.elem/2:
+
+                   elem({1, 2}, -1)
+
+               got the index:
+
+                   -1
+               """
     end
 
     test "Tuple.insert_at/3" do
@@ -858,6 +869,34 @@ defmodule Module.Types.ExprTest do
 
                    {:ok, integer()}
                """
+
+      assert typeerror!([x], Tuple.insert_at({:ok, x}, 3, "foo")) |> strip_ansi() ==
+               ~l"""
+               expected a tuple with at least 3 elements in Tuple.insert_at/3:
+
+                   Tuple.insert_at({:ok, x}, 3, "foo")
+
+               the given type does not have the given index:
+
+                   dynamic({:ok, term()})
+
+               where "x" was given the type:
+
+                   # type: dynamic()
+                   # from: types_test.ex:LINE-1
+                   x
+               """
+
+      assert typeerror!(Tuple.insert_at({1, 2}, -1, :x)) ==
+               ~l"""
+               expected a non-negative integer as index in Tuple.insert_at/3:
+
+                   Tuple.insert_at({1, 2}, -1, :x)
+
+               got the index:
+
+                   -1
+               """
     end
 
     test "Tuple.delete_at/2" do
@@ -897,6 +936,105 @@ defmodule Module.Types.ExprTest do
 
                    {:ok, integer()}
                """
+
+      assert typeerror!([x], Tuple.delete_at({:ok, x}, 2)) |> strip_ansi() ==
+               ~l"""
+               expected a tuple with at least 3 elements in Tuple.delete_at/2:
+
+                   Tuple.delete_at({:ok, x}, 2)
+
+               the given type does not have the given index:
+
+                   dynamic({:ok, term()})
+
+               where "x" was given the type:
+
+                   # type: dynamic()
+                   # from: types_test.ex:LINE-1
+                   x
+               """
+
+      assert typeerror!(Tuple.delete_at({1, 2}, -1)) ==
+               ~l"""
+               expected a non-negative integer as index in Tuple.delete_at/2:
+
+                   Tuple.delete_at({1, 2}, -1)
+
+               got the index:
+
+                   -1
+               """
+    end
+
+    test "put_elem/3" do
+      assert typecheck!(put_elem({:ok, 123}, 0, "foo")) == tuple([binary(), integer()])
+      assert typecheck!(put_elem({:ok, 123}, 1, "foo")) == tuple([atom([:ok]), binary()])
+
+      assert typecheck!([x], put_elem({:ok, x}, 0, "foo")) ==
+               dynamic(tuple([binary(), term()]))
+
+      assert typecheck!([x], put_elem({:ok, x}, 1, "foo")) ==
+               dynamic(tuple([atom([:ok]), binary()]))
+
+      assert typeerror!([<<x::float>>], put_elem(x, 0, "foo")) |> strip_ansi() ==
+               ~l"""
+               incompatible types given to Kernel.put_elem/3:
+
+                   put_elem(x, 0, "foo")
+
+               given types:
+
+                   float(), integer(), binary()
+
+               but expected one of:
+
+                   {...}, integer(), term()
+
+               where "x" was given the type:
+
+                   # type: float()
+                   # from: types_test.ex:LINE-1
+                   <<x::float>>
+               """
+
+      assert typeerror!(put_elem({:ok, 123}, 2, "foo")) ==
+               ~l"""
+               expected a tuple with at least 3 elements in Kernel.put_elem/3:
+
+                   put_elem({:ok, 123}, 2, "foo")
+
+               the given type does not have the given index:
+
+                   {:ok, integer()}
+               """
+
+      assert typeerror!([x], put_elem({:ok, x}, 2, "foo")) |> strip_ansi() ==
+               ~l"""
+               expected a tuple with at least 3 elements in Kernel.put_elem/3:
+
+                   put_elem({:ok, x}, 2, "foo")
+
+               the given type does not have the given index:
+
+                   dynamic({:ok, term()})
+
+               where "x" was given the type:
+
+                   # type: dynamic()
+                   # from: types_test.ex:LINE-1
+                   x
+               """
+
+      assert typeerror!(put_elem({1, 2}, -1, :x)) ==
+               ~l"""
+               expected a non-negative integer as index in Kernel.put_elem/3:
+
+                   put_elem({1, 2}, -1, :x)
+
+               got the index:
+
+                   -1
+               """
     end
 
     test "Tuple.duplicate/2" do