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)
diff --git a/Misc/NEWS b/Misc/NEWS
index 2961776..dd98665 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -36,6 +36,10 @@
 Library
 -------
 
+- Issue #13087: BufferedReader.seek() now always raises UnsupportedOperation
+  if the underlying raw stream is unseekable, even if the seek could be
+  satisfied using the internal buffer.  Patch by John O'Connor.
+
 - Issue #7689: Allow pickling of dynamically created classes when their
   metaclass is registered with copyreg.  Patch by Nicolas M. Thiéry and Craig
   Citro.
diff --git a/Modules/_io/bufferedio.c b/Modules/_io/bufferedio.c
index d6f0c9c..bd1aae5 100644
--- a/Modules/_io/bufferedio.c
+++ b/Modules/_io/bufferedio.c
@@ -1086,6 +1086,9 @@
 
     CHECK_CLOSED(self, "seek of closed file")
 
+    if (_PyIOBase_check_seekable(self->raw, Py_True) == NULL)
+        return NULL;
+
     target = PyNumber_AsOff_t(targetobj, PyExc_ValueError);
     if (target == -1 && PyErr_Occurred())
         return NULL;