Non-Parallelism the axial direction occurs during grinding process of long slender shafts. The reason for the axial error is due to elastic deformation of the components, accumulation phenomenon of the grinding and wheel wear during the grinding process. The accumulation phenomenon, the size generation mechanism and the wheel wear process during traverse grinding result in complicated process at each step on the wheel surface. The grinding system stiffness obtained from the stiffness of the center on the tailstock and the workpiece varing according to the relative position of the wheel and the workpiece. Further more, the value of wheel wear increases as the grinding process advances. The above mentioned issues make the shape generation process during traverse grinding quite complicated. This research analyzes the shape generation process in the direction of the work spindle. First, the formulation of the grinding system stiffness was conducted and the simulation analysis method of the traverse grinding was established. Also, a measuring system for assessing the dimensinal accuracy of the workpiece has been developed.