diff --git a/Tests/test_core_resources.py b/Tests/test_core_resources.py
index d5e358f31..c8ba4b4d5 100644
--- a/Tests/test_core_resources.py
+++ b/Tests/test_core_resources.py
@@ -105,6 +105,8 @@ class TestCoreMemory(PillowTestCase):
             Image.new("RGB", (10, 10))
 
         self.assertRaises(ValueError, Image.core.set_blocks_max, -1)
+        if sys.maxsize < 2 ** 32:
+            self.assertRaises(ValueError, Image.core.set_blocks_max, 2 ** 29)
 
     @unittest.skipIf(is_pypy, "images are not collected")
     def test_set_blocks_max_stats(self):
diff --git a/src/_imaging.c b/src/_imaging.c
index 1391ffae6..dffef3689 100644
--- a/src/_imaging.c
+++ b/src/_imaging.c
@@ -3625,6 +3625,12 @@ _set_blocks_max(PyObject* self, PyObject* args)
             "blocks_max should be greater than 0");
         return NULL;
     }
+    else if ( blocks_max > SIZE_MAX/sizeof(ImagingDefaultArena.blocks_pool[0])) {
+        PyErr_SetString(PyExc_ValueError,
+            "blocks_max is too large");
+        return NULL;
+    }
+
 
     if ( ! ImagingMemorySetBlocksMax(&ImagingDefaultArena, blocks_max)) {
         ImagingError_MemoryError();