Geometric　errors　directly　affect　the　tool　tip　position,　reduce　machining　accuracy,　and　are　one　of　the　most　important　errors　of　multi-axis　machining　tool.　However,　the　geometric　errors　are　intercoupling,　and　the　measured　values　at　different　points　vary　and　are　stochastic.　The　identification　of　the　most　crucial　geometric　errors　and　the　determination　of　a　method　to　control　them　is　a　key　problem　to　improve　the　machining　accuracy　of　machine　tool.　To　achieve　this　goal,　a　new　analytical　method,　to　identify　crucial　geometric　errors　for　a　multi-axis　machine　tool　is　proposed　here　based　on　multibody　system　(MBS)　theory　and　global　sensitivity　analysis.　The　volumetric　error　modeling　of　multi-axis　machine　tool　has　been　given　by　MBS　theory,　which　describes　the　topological　structure　of　multibody　system　simply　and　conveniently　in　a　matrix.　The　stochastic　characteristic　of　geometric　errors　is　taken　into　consideration　and　Sobol　global　sensitivity　analysis　method　is　introduced　to　identify　crucial　geometric　errors　of　machine　tool.　A　vertical　machining　center　is　selected　as　an　illustration　example.　The　analysis　results　reveal　that　the　analytical　method　presented　in　this　paper　can　identify　the　crucial　geometric　errors　and　are　helpful　to　improve　the　machining　accuracy　of　multi-axis　machine　tool.