diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index 0dc9d6d..53cabbb 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -922,6 +922,14 @@
         finally:
             support.unlink(support.TESTFN)
 
+    def test_unseekable(self):
+        bufio = self.tp(self.MockUnseekableIO(b"A" * 10))
+        self.assertRaises(self.UnsupportedOperation, bufio.tell)
+        self.assertRaises(self.UnsupportedOperation, bufio.seek, 0)
+        bufio.read(1)
+        self.assertRaises(self.UnsupportedOperation, bufio.seek, 0)
+        self.assertRaises(self.UnsupportedOperation, bufio.tell)
+
     def test_misbehaved_io(self):
         rawio = self.MisbehavedRawIO((b"abc", b"d", b"efg"))
         bufio = self.tp(rawio)