Geometric　error　has　significant　influence　on　the　processing　results　and　reduces　machining　accuracy.　Machine　tool　geometric　errors　can　be　interpreted　as　a　deterministic　value　with　an　uncertain　fluctuation　of　probabilistic　distribution.　Although,　the　uncertain　fluctuation　can　not　be　compensated,　it　has　extremely　profound　significance　on　the　precision　and　ultra-precision　machining　to　reduce　the　fluctuation　range　of　machining　accuracy　as　far　as　possible.　In　this　paper,　a　typical　3-axis　machine　tool　with　high　precision　is　selected　and　the　fluctuations　in　machining　accuracy　are　studied.　The　volumetric　error　modeling　of　machine　tool　is　established　by　multi-body　system　(MBS)　theory,　which　describes　the　topological　structure　of　MBS　in　a　simple　and　convenient　matrix　form.　Based　on　the　volumetric　error　model,　the　equivalent　components　of　the　errors　for　the　three　axes　are　established　by　reducing　error　terms.　Then,　the　fluctuations　of　equivalent　errors　and　the　machining　accuracy　in　working　planes　are　depicted　and　predicted　using　the　theory　of　stochastic　process,　whose　range　should　be　controlled　within　a　certain　confidence　interval.　Furthermore,　the　critical　geometric　errors　that　have　significant　influence　on　the　machining　accuracy　fluctuation　are　identified.　Based　on　the　analysis　results,　some　improvement　in　the　machine　tool　parts　introduced　and　the　results　for　the　modified　machine　show　that　the　prediction　allow　for　reduction　in　errors　for　the　precision　and　ultra-precision　machining.