Functional　tolerancing　of　mechanisms　has　now　been　well　accepted　in　industry　and　become　a　major　concern　for　academia.　After　a　brief　comparison　of　existing　3D　functional　tolerance　analysis　models,　a　statistical　tolerancing　approach　based　on　variation　of　pointset　is　proposed　in　this　paper.　The　toleranced　surface　is　represented　by　a　point-set　which　is　consistent　with　its　parametric　equations,　the　semantics　of　geometrical　tolerances　are　parameterized　with　respect　to　variation　of　point-set　and　associated　mathematical　interpretations　of　tolerance　zone　are　formalized.　Three　methods　are　presented　to　extract　individual　points　from　point-set:　characteristic　points　of　MGRE,　characteristic　points　of　geometrical　surface　and　discrete　points　of　geometrical　surface.　The　tolerance　chains　through　key　assembly　features　are　analyzed　and　represented　by　homogenous　transform　matrix.　The　over-constrained　degrees　of　freedom　of　a　complex　junction　with　multiple　mating　features　are　taken　into　account　in　accordance　with　datum　precedence.　The　approach　is　applied　to　statistical　tolerance　analysis　of　a　coordinate　measuring　machine　to　analyze　deviation　distribution　of　a　geometrical　functional　requirement　on　the　ending　geometric　feature.　©　2013　The　Authors.