diff --git a/Lib/test/test_platform.py b/Lib/test/test_platform.py
index f167fb1e7b9..0e6cb6db1ee 100644
--- a/Lib/test/test_platform.py
+++ b/Lib/test/test_platform.py
@@ -3,6 +3,8 @@
 import subprocess
 import sys
 import unittest
+import collections
+import contextlib
 from unittest import mock
 
 from test import support
@@ -160,6 +162,18 @@ def test_uname(self):
         self.assertEqual(res[4], res.machine)
         self.assertEqual(res[5], res.processor)
 
+    @unittest.skipIf(sys.platform in ['win32', 'OpenVMS'], "uname -p not used")
+    def test_uname_processor(self):
+        """
+        On some systems, the processor must match the output
+        of 'uname -p'. See Issue 35967 for rationale.
+        """
+        with contextlib.suppress(subprocess.CalledProcessError):
+            self.assertEqual(
+                platform.uname().processor,
+                subprocess.check_output(['uname', '-p'], text=True).strip(),
+            )
+
     @unittest.skipUnless(sys.platform.startswith('win'), "windows only test")
     def test_uname_win32_ARCHITEW6432(self):
         # Issue 7860: make sure we get architecture from the correct variable