Computer　numerical　controlled　(CNC)　machine　tools　are　comprised　of　numerous　parts　mainly　connected　by　bolts.　Accurate　modeling　of　the　contact　stiffness　of　bolted　joints　is　therefore　a　crucial　element　in　predicting　the　dynamic　performance　of　CNC　machine　tools.　This　paper　presents　a　contact　stiffness　model　of　a　bolted　joint　based　on　multi-scale　theory.　The　model　uses　a　series　of　stacked　three-dimensional　sine　waves　to　describe　the　multi-scale　roughness　of　the　contact　surface,　and　each　frequency　level　is　considered　to　be　a　single　layer　of　asperities,　which　are　stacked　on　top　of　each　other.　A　relationship　between　the　contact　area　ratio　and　frequency　level　can　be　deduced.　Moreover,　the　contact　stiffness　at　each　frequency　level　can　be　represented　within　the　model　as　a　spring　in　series,　therefore,　the　total　stiffness　is　obtained　by　summing　the　contact　stiffness　at　each　frequency　level.　An　experimental　setup　consisting　of　a　box-shaped　specimen　was　used　to　validate　the　numerical　model　of　the　bolted　joint　for　the　case　of　equal　bolt　pre-tightening　forces　and　relative　errors　between　the　multi-scale　natural　frequencies　and　experimental　frequencies　were　found　to　be　less　than　5.91%.　This　suggests　the　multi-scale　model　can　be　used　to　effectively　predict　the　dynamic　characteristics　of　CNC　machine　tools.　©　2020,　Chinese　Mechanical　Engineering　Society.　All　right　reserved.