The three axis CNC grinding machine tool for ultra-Precision mirror surface grinding of advanced materials such as ceramics and other hard and brittle materials was designed. The grinding machine is composed of the air spindle, the high damping resin concrete bed, and the three axis CNC contoller with the high resolution AC servo motor.4 new method of modeling for the linear motion guide and the ball screw using three dimensional finite element method was introduced. From the comparison between the analytical results and the experimental results, it was found that the modeling method gave accurate results in the prediction of the stiffness of machine tools. Based on the results, the prototype three axis CNC grinding machine was manufactured. To investigate the dynamic properties of the grinding machine, the natural frequency and damping of the spindle and the headstock were experimentally measured. Also the mode shape of the table at the first natural frequency was experimentally obtained.