diff --git a/include/pybind11/cast.h b/include/pybind11/cast.h
index 69c07bef1..b04083e2f 100644
--- a/include/pybind11/cast.h
+++ b/include/pybind11/cast.h
@@ -889,7 +889,7 @@ struct handle_type_name<dict> {
 };
 template <>
 struct handle_type_name<anyset> {
-    static constexpr auto name = const_name("set | frozenset");
+    static constexpr auto name = const_name("Union[set, frozenset]");
 };
 template <>
 struct handle_type_name<set> {
diff --git a/tests/test_pytypes.py b/tests/test_pytypes.py
index cd082cdea..87d5d5518 100644
--- a/tests/test_pytypes.py
+++ b/tests/test_pytypes.py
@@ -121,7 +121,7 @@ def test_set(capture, doc):
     assert m.anyset_contains({"foo"}, "foo")
 
     assert doc(m.get_set) == "get_set() -> set"
-    assert doc(m.print_anyset) == "print_anyset(arg0: set | frozenset) -> None"
+    assert doc(m.print_anyset) == "print_anyset(arg0: Union[set, frozenset]) -> None"
 
 
 def test_frozenset(capture, doc):