diff --git a/graalpython/com.oracle.graal.python.test/src/tests/test_mmap.py b/graalpython/com.oracle.graal.python.test/src/tests/test_mmap.py
index 41f9d78738..082966834a 100644
--- a/graalpython/com.oracle.graal.python.test/src/tests/test_mmap.py
+++ b/graalpython/com.oracle.graal.python.test/src/tests/test_mmap.py
@@ -1,4 +1,4 @@
-# Copyright (c) 2024, Oracle and/or its affiliates. All rights reserved.
+# Copyright (c) 2024, 2026, Oracle and/or its affiliates. All rights reserved.
 # DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 #
 # The Universal Permissive License (UPL), Version 1.0
@@ -38,11 +38,25 @@
 # SOFTWARE.
 
 import mmap
+import sys
 
 PAGESIZE = mmap.PAGESIZE
 FIND_BUFFER_SIZE = 1024  # keep in sync with FindNode#BUFFER_SIZE
 
 
+def test_map_private_constant_matches_platform():
+    assert hasattr(mmap, "MAP_PRIVATE") == (sys.platform != "win32")
+
+
+def test_access_copy_without_map_private_constant():
+    m = mmap.mmap(-1, 1, access=mmap.ACCESS_COPY)
+    try:
+        m[0] = b'a'[0]
+        assert m[:] == b'a'
+    finally:
+        m.close()
+
+
 def test_find():
     cases = [
         # (size, needle_pos)
@@ -103,4 +117,4 @@ def test_iter():
     for i in m:
         l.append(i)
 
-    assert l == [b'\x02', b'\x03', b'\x04']
\ No newline at end of file
+    assert l == [b'\x02', b'\x03', b'\x04']
diff --git a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/mmap/MMapBuiltins.java b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/mmap/MMapBuiltins.java
index 5e12562602..a0c127f9c3 100644
--- a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/mmap/MMapBuiltins.java
+++ b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/mmap/MMapBuiltins.java
@@ -226,7 +226,7 @@ static PMMap doFile(VirtualFrame frame, Object clazz, int fd, long lengthIn, int
                     prot = PROT_READ.value | PROT_WRITE.value;
                     break;
                 case ACCESS_COPY:
-                    flags = MAP_PRIVATE.value;
+                    flags = MAP_PRIVATE.defined ? MAP_PRIVATE.getValueIfDefined() : 0;
                     prot = PROT_READ.value | PROT_WRITE.value;
                     break;
                 case PMMap.ACCESS_DEFAULT:
diff --git a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstants.java b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstants.java
index dd8ce720cf..91a913a6d2 100644
--- a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstants.java
+++ b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstants.java
@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 2021, 2025, Oracle and/or its affiliates. All rights reserved.
+ * Copyright (c) 2021, 2026, Oracle and/or its affiliates. All rights reserved.
  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
  *
  * The Universal Permissive License (UPL), Version 1.0
@@ -150,7 +150,7 @@ public final class PosixConstants {
     public static final MandatoryIntConstant S_IFCHR;
     public static final MandatoryIntConstant S_IFIFO;
     public static final MandatoryIntConstant MAP_SHARED;
-    public static final MandatoryIntConstant MAP_PRIVATE;
+    public static final OptionalIntConstant MAP_PRIVATE;
     public static final MandatoryIntConstant MAP_ANONYMOUS;
     public static final OptionalIntConstant MAP_DENYWRITE;
     public static final OptionalIntConstant MAP_EXECUTABLE;
@@ -483,7 +483,7 @@ public final class PosixConstants {
         S_IFCHR = reg.createMandatoryInt("S_IFCHR");
         S_IFIFO = reg.createMandatoryInt("S_IFIFO");
         MAP_SHARED = reg.createMandatoryInt("MAP_SHARED");
-        MAP_PRIVATE = reg.createMandatoryInt("MAP_PRIVATE");
+        MAP_PRIVATE = reg.createOptionalInt("MAP_PRIVATE");
         MAP_ANONYMOUS = reg.createMandatoryInt("MAP_ANONYMOUS");
         MAP_DENYWRITE = reg.createOptionalInt("MAP_DENYWRITE");
         MAP_EXECUTABLE = reg.createOptionalInt("MAP_EXECUTABLE");
diff --git a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstantsWin32.java b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstantsWin32.java
index 1ce31c2371..7233591050 100644
--- a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstantsWin32.java
+++ b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/runtime/PosixConstantsWin32.java
@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 2021, 2025, Oracle and/or its affiliates. All rights reserved.
+ * Copyright (c) 2021, 2026, Oracle and/or its affiliates. All rights reserved.
  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
  *
  * The Universal Permissive License (UPL), Version 1.0
@@ -85,7 +85,6 @@ static void getConstants(PosixConstants.Registry constants) {
         constants.put("S_IFCHR", 0x00002000);
         constants.put("S_IFIFO", 0);
         constants.put("MAP_SHARED", 1);
-        constants.put("MAP_PRIVATE", 2);
         constants.put("MAP_ANONYMOUS", 4);
         constants.put("PROT_NONE", 0);
         constants.put("PROT_READ", 1);
diff --git a/scripts/gen_native_cfg.py b/scripts/gen_native_cfg.py
index 5e7b7fd9f0..e2f2264fac 100644
--- a/scripts/gen_native_cfg.py
+++ b/scripts/gen_native_cfg.py
@@ -1,4 +1,4 @@
-# Copyright (c) 2021, 2025, Oracle and/or its affiliates. All rights reserved.
+# Copyright (c) 2021, 2026, Oracle and/or its affiliates. All rights reserved.
 # DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 #
 # The Universal Permissive License (UPL), Version 1.0
@@ -209,7 +209,7 @@
 
 [mmapFlags]
 1 x MAP_SHARED
-2 x MAP_PRIVATE
+* x MAP_PRIVATE
 4 x MAP_ANONYMOUS
 * x MAP_DENYWRITE
 * x MAP_EXECUTABLE