diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 385dbb536d8a7d..844a2aa25fdccf 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -2174,7 +2174,9 @@ def getmember(self, name):
            than once in the archive, its last occurrence is assumed to be the
            most up-to-date version.
         """
-        tarinfo = self._getmember(name.rstrip('/'))
+        tarinfo = self._getmember(name)
+        if tarinfo is None and name.endswith('/'):
+            tarinfo = self._getmember(name.rstrip('/'))
         if tarinfo is None:
             raise KeyError("filename %r not found" % name)
         return tarinfo
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 2998a3667b4d17..692f97d1f71130 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -254,6 +254,14 @@ def test_add_dir_getmember(self):
         self.add_dir_and_getmember('bar')
         self.add_dir_and_getmember('a'*101)
 
+    def test_extract_name_with_trailing_slash(self):
+        with tarfile.open(tmpname, 'w') as tar:
+            tar.addfile(tarfile.TarInfo('./mydir/'))
+        with tarfile.open(tmpname) as tar:
+            names = tar.getnames()
+            self.assertEqual(names, ['./mydir/'])
+            tar.extract(names[0], TEMPDIR, filter='fully_trusted')
+
     @unittest.skipUnless(hasattr(os, "getuid") and hasattr(os, "getgid"),
                          "Missing getuid or getgid implementation")
     def add_dir_and_getmember(self, name):
diff --git a/Misc/NEWS.d/next/Library/2026-07-04-00-19-23.gh-issue-127636.o_uD9U.rst b/Misc/NEWS.d/next/Library/2026-07-04-00-19-23.gh-issue-127636.o_uD9U.rst
new file mode 100644
index 00000000000000..51957a73b5603b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-07-04-00-19-23.gh-issue-127636.o_uD9U.rst
@@ -0,0 +1,3 @@
+Fix :meth:`tarfile.TarFile.extract` to accept archive member names with a
+trailing forward slash, including those returned by
+:meth:`tarfile.TarFile.getnames`. Contributed by Xiao Yuan.