diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index c83af0d..b77dda5 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -1043,6 +1043,10 @@
 				    "mmap invalid access parameter.");
 	}
 
+    if (prot == PROT_READ) {
+        access = ACCESS_READ;
+    }
+
 #ifdef HAVE_FSTAT
 #  ifdef __VMS
 	/* on OpenVMS we must ensure that all bytes are written to the file */