A finite element method (FEM) for predicting the temperature and stress distribution is presented. Two workpiece materials were carried out, one is Al7050-T6 the other is Ti-6Al-4V. The flow stress of workpiece material is taken as a function of strain, strain rate and temperature in order to reflect realistic behavior in machining process. Diamond cutting tool with rake angle 50, clearance angle 100, and cutting edge radius 1 is used. From simulation, cutting force, thrust force, and distribution of cutting temperature and stress are obtained.