diff --git a/rest_framework/routers.py b/rest_framework/routers.py
index 2b9478e90..523214d6e 100644
--- a/rest_framework/routers.py
+++ b/rest_framework/routers.py
@@ -136,7 +136,12 @@ class SimpleRouter(BaseRouter):
     ]
 
     def __init__(self, trailing_slash=True, use_regex_path=True):
-        self.trailing_slash = '/' if trailing_slash else ''
+        if trailing_slash is True:
+            self.trailing_slash = '/'
+        elif trailing_slash is False:
+            self.trailing_slash = ''
+        else:
+            self.trailing_slash = "/?"
         self._use_regex = use_regex_path
         if use_regex_path:
             self._base_pattern = '(?P<{lookup_prefix}{lookup_url_kwarg}>{lookup_value})'
diff --git a/tests/test_routers.py b/tests/test_routers.py
index 887f601d5..7e60f2c24 100644
--- a/tests/test_routers.py
+++ b/tests/test_routers.py
@@ -328,6 +328,21 @@ class TestTrailingSlashRemoved(TestCase):
             assert expected[idx] == self.urls[idx].pattern.regex.pattern
 
 
+class TestTrailingSlashOptional(TestCase):
+    def setUp(self):
+        class NoteViewSet(viewsets.ModelViewSet):
+            queryset = RouterTestModel.objects.all()
+
+        self.router = SimpleRouter(trailing_slash=None)
+        self.router.register(r'notes', NoteViewSet)
+        self.urls = self.router.urls
+
+    def test_urls_have_trailing_slash_by_default(self):
+        expected = ['^notes/?$', '^notes/(?P<pk>[^/.]+)/?$']
+        for idx in range(len(expected)):
+            assert expected[idx] == self.urls[idx].pattern.regex.pattern
+
+
 class TestNameableRoot(TestCase):
     def setUp(self):
         class NoteViewSet(viewsets.ModelViewSet):