diff --git a/autotest/gdrivers/jp2kak.py b/autotest/gdrivers/jp2kak.py
index 4b1c169ec291..63cc74f1fd39 100755
--- a/autotest/gdrivers/jp2kak.py
+++ b/autotest/gdrivers/jp2kak.py
@@ -456,6 +456,51 @@ def test_jp2kak_lossless_uint32_nbits_20():
     gdal.GetDriverByName("JP2KAK").Delete(tmpfilename)
 
 
+###############################################################################
+# Test lossless copying of multi band with tiling (to cause a stripe_height != 1)
+
+
+@pytest.mark.parametrize("use_stripe_compressor", ["YES", "NO"])
+def test_jp2kak_lossless_multiband(tmp_vsimem, use_stripe_compressor):
+
+    src_ds = gdal.Open("data/rgbsmall.tif")
+    out_filename = str(tmp_vsimem / "out.jp2")
+    with gdaltest.config_option("JP2KAK_USE_STRIPE_COMPRESSOR", use_stripe_compressor):
+        gdal.GetDriverByName("JP2KAK").CreateCopy(
+            out_filename,
+            src_ds,
+            options=["QUALITY=100", "BLOCKXSIZE=32", "BLOCKYSIZE=24"],
+        )
+    ds = gdal.Open(out_filename)
+    assert [ds.GetRasterBand(i + 1).Checksum() for i in range(3)] == [
+        src_ds.GetRasterBand(i + 1).Checksum() for i in range(3)
+    ]
+
+
+###############################################################################
+# Test lossless copying of multi band with tiling (to cause a stripe_height != 1)
+
+
+@pytest.mark.parametrize("use_stripe_compressor", ["YES", "NO"])
+def test_jp2kak_lossless_multiband_non_byte(tmp_vsimem, use_stripe_compressor):
+
+    src_ds = gdal.Open("data/rgbsmall.tif")
+    src_ds = gdal.Translate(
+        "", src_ds, options="-f MEM -ot UInt16 -scale 0 255 0 65535"
+    )
+    out_filename = str(tmp_vsimem / "out.jp2")
+    with gdaltest.config_option("JP2KAK_USE_STRIPE_COMPRESSOR", use_stripe_compressor):
+        gdal.GetDriverByName("JP2KAK").CreateCopy(
+            out_filename,
+            src_ds,
+            options=["QUALITY=100", "BLOCKXSIZE=32", "BLOCKYSIZE=24"],
+        )
+    ds = gdal.Open(out_filename)
+    assert [ds.GetRasterBand(i + 1).Checksum() for i in range(3)] == [
+        src_ds.GetRasterBand(i + 1).Checksum() for i in range(3)
+    ]
+
+
 ###############################################################################
 # Test lossy copying of Int32
 
diff --git a/frmts/jp2kak/jp2kakdataset.cpp b/frmts/jp2kak/jp2kakdataset.cpp
index ad1e994ca9be..3ed7ab2fb72d 100644
--- a/frmts/jp2kak/jp2kakdataset.cpp
+++ b/frmts/jp2kak/jp2kakdataset.cpp
@@ -2903,7 +2903,9 @@ static GDALDataset *JP2KAKCreateCopy(const char *pszFilename,
         std::vector<int> precisions(num_components);
         for (int i = 0; i < num_components; ++i)
         {
-            stripe_bufs[i] = pBuffer + nXSize * nDataTypeSizeBytes * i;
+            stripe_bufs[i] = pBuffer + static_cast<size_t>(nXSize) *
+                                           nDataTypeSizeBytes * i *
+                                           stripe_height;
             is_signed[i] = CPL_TO_BOOL(GDALDataTypeIsSigned(eType));
             precisions[i] = nBits;
         }
@@ -2918,6 +2920,9 @@ static GDALDataset *JP2KAKCreateCopy(const char *pszFilename,
                 for (int i = 0; i < num_components; ++i)
                 {
                     stripe_heights[i] = nHeight;
+                    stripe_bufs[i] = pBuffer + static_cast<size_t>(nXSize) *
+                                                   nDataTypeSizeBytes * i *
+                                                   nHeight;
                 }
             }
             if (poSrcDS->RasterIO(GF_Read, 0, iY, nXSize, nHeight, pBuffer,