diff --git a/pandas-stubs/core/arrays/base.pyi b/pandas-stubs/core/arrays/base.pyi
index 7141f70ff..9a6327008 100644
--- a/pandas-stubs/core/arrays/base.pyi
+++ b/pandas-stubs/core/arrays/base.pyi
@@ -56,6 +56,10 @@ class ExtensionArray:
     def view(self, dtype=...) -> Self | np.ndarray: ...
     def ravel(self, order=...) -> Self: ...
     def tolist(self) -> list: ...
+    def _reduce(
+        self, name: str, *, skipna: bool = ..., keepdims: bool = ..., **kwargs
+    ) -> object: ...
+    def _accumulate(self, name: str, *, skipna: bool = ..., **kwargs) -> Self: ...
 
 class ExtensionOpsMixin:
     @classmethod
diff --git a/tests/test_extension.py b/tests/test_extension.py
index 6784819dd..a8e34c171 100644
--- a/tests/test_extension.py
+++ b/tests/test_extension.py
@@ -1,6 +1,8 @@
 import decimal
 
+import numpy as np
 import pandas as pd
+from pandas.arrays import IntegerArray
 from typing_extensions import assert_type
 
 from tests import check
@@ -25,3 +27,12 @@ def test_tolist() -> None:
     check(assert_type(s.array.tolist(), list), list)
     check(assert_type(s1.array.tolist(), list), list)
     check(assert_type(pd.array([1, 2, 3]).tolist(), list), list)
+
+
+def test_ExtensionArray_reduce_accumulate() -> None:
+    _data = IntegerArray(
+        values=np.array([1, 2, 3], dtype=int),
+        mask=np.array([True, False, False], dtype=bool),
+    )
+    check(assert_type(_data._reduce("max"), object), np.integer)
+    check(assert_type(_data._accumulate("cumsum"), IntegerArray), IntegerArray)