As　the　geometric　errors　of　motion　axis　can　be　equivalent　to　the　differential　movement,　regarded　as　a　differential　operator　based　on　its　ideal　position,　a　new　modeling　method　for　multi-axis　CNC　machines　based　on　differential　transform　theory　is　proposed　in　this　paper.　First,　the　workpiece　coordinates　is　selected　to　observe　the　errors　of　the　tool　pose.　Then,　a　general　geometric　error　model　for　multi-axis　machines　is　established.　Moreover,　the　Jacobian　matrix　is　applied　to　describe　the　relationship　between　the　tool　pose　error　vector　and　the　compensation　error　vector.　All　the　elements　of　the　matrix　are　obtained　by　computing　the　differential　operators　instead　of　computing　the　partial　derivatives.　The　compensation　errors　vector　is　solved　using　the　pseudo-inverse　Jacobian　matrix.　Finally,　an　automatic　modeling　procedure　is　developed　to　construct　the　geometric　errors　for　multi-axis　machine　tools.　An　experiment　on　a　five-axis　machine　tool　is　conducted　to　test　and　verify　the　proposed　method.　The　results　show　that　the　proposed　method　dramatically　improves　the　overall　position　accuracy　of　the　test　tool　path.　©　2013　Springer-Verlag　London.