The　ensemble　static　stiffness　of　machine　tool　is　its　ability　to　maintain　smooth　working　condition　and　resist　a　variety　of　loads.　As　the　dispensable　part　of　ensemble　static　stiffness,　critical　components　stiffness　plays　a　significant　role　in　the　performance　of　the　ultra-precision　grinding　machine　tool.　In　this　paper,　a　three-axis　CNC　grinding　machine　tool　for　the　ultra-precision　mirror　surface　grinding　of　advanced　materials　such　as　ceramics　and　other　hard　and　brittle　materials　has　been　designed.　And　the　stiffness　and　modal　parameters　of　the　grinding　machine　tool　are　discussed　using　finite　element　software.　The　results　are　presented　and　discussed　thoroughly.　This　in　turn　can　help　to　revise　design　defects　and　reduce　research　and　develop　costs.