The　static　stiffness　of　machine　tools　can　be　used　for　the　analysis　of　thermal　deformation　because　of　the　uneven　temperature　field　and　can　further　be　applied　in　the　thermal　error　compensation.　The　prediction　of　static　performance　of　machine　tools　is　fundamental　and　essential　during　the　design　period.　The　purpose　of　this　paper　is　to　establish　a　precise　static　stiffness　model　for　machine　tools.　Different　from　previous　models,　the　proposed　method　in　this　paper,　basing　on　the　Fractal　Geometry,　takes　both　the　elastoplastic　deformation　mechanism　and　friction　into　account.　By　analyzing　the　normal　stiffness　and　tangential　stiffness　of　joints,　equivalent　virtual　material　parameters　are　acquired　for　the　finite　element　analysis　calculation.　An　experimental　set-up　has　been　established　to　test　X,　Y　and　Z　directional　deformation　of　a　vertical　machine　center　with　a　magnitude　of　200 kgf　load　applied　to　the　node　of　the　spindle　along　the　respective　direction.　The　results　demonstrate　that　the　proposed　model　can　accurately　simulate　static　characteristics　of　machine　tools.　©　2020,　The　Brazilian　Society　of　Mechanical　Sciences　and　Engineering.