diff --git a/lib/elixir/lib/module/types/apply.ex b/lib/elixir/lib/module/types/apply.ex
index 13d96127012..8f941e4124e 100644
--- a/lib/elixir/lib/module/types/apply.ex
+++ b/lib/elixir/lib/module/types/apply.ex
@@ -435,6 +435,12 @@ defmodule Module.Types.Apply do
     end
   end
 
+  defp do_remote(:erlang, :element, [index, tuple], _expected, expr, stack, context, of_fun)
+       when is_integer(index) and index < 1 do
+    {_, context} = of_fun.(tuple, open_tuple([]), expr, stack, context)
+    remote_error({:negindex, index - 1}, :erlang, :element, 2, expr, stack, context)
+  end
+
   defp do_remote(:erlang, :element, [index, tuple], expected, expr, stack, context, of_fun)
        when is_integer(index) do
     tuple_type = open_tuple(List.duplicate(term(), max(index - 1, 0)) ++ [expected])
@@ -458,6 +464,13 @@ defmodule Module.Types.Apply do
     {return(tuple(List.duplicate(elem_type, size)), [elem_type], stack), context}
   end
 
+  defp do_remote(:erlang, :insert_element, [index, tuple, elem], _, expr, stack, context, of_fun)
+       when is_integer(index) and index < 1 do
+    {_, context} = of_fun.(tuple, open_tuple([]), expr, stack, context)
+    {_, context} = of_fun.(elem, term(), expr, stack, context)
+    remote_error({:negindex, index - 1}, :erlang, :insert_element, 3, expr, stack, context)
+  end
+
   defp do_remote(:erlang, :insert_element, [index, tuple, elem], _, expr, stack, context, of_fun)
        when is_integer(index) do
     tuple_type = open_tuple(List.duplicate(term(), max(index - 1, 0)))
@@ -479,6 +492,12 @@ defmodule Module.Types.Apply do
     end
   end
 
+  defp do_remote(:erlang, :delete_element, [index, tuple], _, expr, stack, context, of_fun)
+       when is_integer(index) and index < 1 do
+    {_, context} = of_fun.(tuple, open_tuple([]), expr, stack, context)
+    remote_error({:negindex, index - 1}, :erlang, :delete_element, 2, expr, stack, context)
+  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)))
@@ -1807,6 +1826,29 @@ 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/test/elixir/module/types/expr_test.exs b/lib/elixir/test/elixir/module/types/expr_test.exs
index 5842f53fc35..5ace329d3a5 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 +869,17 @@ defmodule Module.Types.ExprTest do
 
                    {:ok, integer()}
                """
+
+      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 +919,17 @@ defmodule Module.Types.ExprTest do
 
                    {:ok, integer()}
                """
+
+      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 "Tuple.duplicate/2" do