diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 3c59eac5d9a0f11..8f5573cba3cd17e 100755
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -2127,7 +2127,9 @@ 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 86fe8efac2e3495..fbb0a3cd8fb003a 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -242,6 +242,19 @@ 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):
+        # gh-127636: './mydir/' is deliberately a regular-file member
+        # (REGTYPE, not DIRTYPE) whose stored name ends in a slash.  It
+        # extracts as a file.  Do not "fix" this by setting DIRTYPE; the
+        # trailing-slash name on a non-directory is what is being tested.
+        with tarfile.open(tmpname, 'w') as tar:
+            tar.addfile(tarfile.TarInfo('./mydir/'))
+        with os_helper.temp_dir() as tmpdir, tarfile.open(tmpname) as tar:
+            names = tar.getnames()
+            self.assertEqual(names, ['./mydir/'])
+            tar.extract(names[0], tmpdir, filter='fully_trusted')
+            self.assertTrue(os.path.isfile(os.path.join(tmpdir, 'mydir')))
+
     @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 000000000000000..51957a73b5603b2
--- /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.