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. The grinding machine is composed of the air spindle, a high-damping resin concrete bed, and a three-axis CNC controller with high resolution AC servo motors, For the stiffness calculations of the grinding machine, a new modeling method for linear motion guides and ball screws using the three dimensional finite-element method was introduced. From comparison of the calculated results with the experimental results, it was found that the modeling method gives accurate results in the prediction of the stiffness of machine tools. Based on the results, a prototype three-axis CNC grinding machine was designed and manufactured, To investigate the dynamic properties of the grinding machine, the natural frequencies and damping of the spindle and the headstock were measured experimentally. Also, the mode shape of the machine tool x-table at the first natural frequency was obtained experimentally, From the grinding operation of ceramic materials. it was found that the prototype grinding machine tool produced mirror surfaces on aluminum oxide and titanium carbide, with arithmetic surface roughnesses of less than 50 nm. (C) 1997 Elsevier Science S.A.