diff --git a/Lib/test/test_os.py b/Lib/test/test_os.py
--- a/Lib/test/test_os.py
+++ b/Lib/test/test_os.py
@@ -28,6 +28,11 @@ try:
     import threading
 except ImportError:
     threading = None
+try:
+    import resource
+except ImportError:
+    resource = None
+
 from test.script_helper import assert_python_ok
 
 with warnings.catch_warnings():
@@ -997,6 +1002,21 @@ class URandomTests(unittest.TestCase):
         data2 = self.get_urandom_subprocess(16)
         self.assertNotEqual(data1, data2)
 
+    @unittest.skipUnless(resource, "test requires the resource module")
+    def test_urandom_failure(self):
+        soft_limit, hard_limit = resource.getrlimit(resource.RLIMIT_NOFILE)
+        resource.setrlimit(resource.RLIMIT_NOFILE, (1, hard_limit))
+        try:
+            with self.assertRaises(OSError) as cm:
+                os.urandom(16)
+            self.assertEqual(cm.exception.errno, errno.EMFILE)
+        finally:
+            # We restore the old limit as soon as possible.  If doing it
+            # using addCleanup(), code running in between would fail
+            # creating any file descriptor.
+            resource.setrlimit(resource.RLIMIT_NOFILE, (soft_limit, hard_limit))
+
+
 @contextlib.contextmanager
 def _execvpe_mockup(defpath=None):
     """
diff --git a/Python/random.c b/Python/random.c
--- a/Python/random.c
+++ b/Python/random.c
@@ -165,8 +165,12 @@ dev_urandom_python(char *buffer, Py_ssiz
     Py_END_ALLOW_THREADS
     if (fd < 0)
     {
-        PyErr_SetString(PyExc_NotImplementedError,
-                        "/dev/urandom (or equivalent) not found");
+        if (errno == ENOENT || errno == ENXIO ||
+            errno == ENODEV || errno == EACCES)
+            PyErr_SetString(PyExc_NotImplementedError,
+                            "/dev/urandom (or equivalent) not found");
+        else
+            PyErr_SetFromErrno(PyExc_OSError);
         return -1;
     }