In the process of grinding a long slender type workpiece, such as ballscrew, by the external cylindrical grinding machine, the cylindricity of the workpiece depends on the distance of rests, the stiffness of supports, the diameter and material of workpiece. Conventionally the process needs to be supported by one or more rests to prevent static deflection and vibration. In this paper, the optimal position of the rests was investigated in order to minimize the cylindricity due to the static deflection, by taking compliance of the workpiece and structure into account. In order to obtain the optimal position of rests, a new modeling that is considering the spring effect of all support elements was established. Since it is so complicated to obtain the optimal position analytically for various conditions due to discontinuity, a genetic algorithm u as utilized.