The　machining　accuracy　of　NC　machine　can　be　improved　significantly　through　the　error　compensation.　The　kernels　of　(multi-body　system)MBS　theories　are　that　the　number　arrays　of　low-order　body　are　used　to　describe　the　topological　structures　which　are　taken　to　generalize　and　refine　MBS,　and　the　characteristic　matrix　are　employed　to　represent　the　relative　positions　and　gestures　between　any　two　bodies　in　MBS.　Based　on　the　theory　of　rigid　body　dynamics　and　homogeneous　coordinate　transformation　techniques,　the　space　error　model　of　five-axis　gantry　NC　machine　can　be　established,　the　modified　NC　instructions　can　be　obtained　and　it　prepares　well　ready　for　the　software　error　compensation　and　the　practical　application.　Gyratory　motion　of　five-axis　NC　machine　will　generate　the　coupling　of　translational　motion,　so　it　is　different　from　the　three-axis　NC　machine　in　the　process　of　error　compensation　and　we　need　to　decoupling.　©　(2013)　Trans　Tech　Publications,　Switzerland.