This paper presents the numerical calculation of the relative sliding distance between the pad and the wafer in a rotary-type chemical-mechanical planarization (CMP) system. The numerical scheme developed in this paper considered most of the possible kinematical and geometrical variables. While the pad was rotating, and the wafer was rotating and sweeping, the point trajectories on the wafer were calculated by standard coordinate transformations. The effect of groove patterns on the pad surface was investigated for the relative sliding distance of the wafer. Three types of pad surface geometries, namely flat, circular-type, and rectangular-type grooves, were considered. From the simulation results, we evaluated the nonuniformity (NU) of the relative sliding distance distribution on the polished wafer surface. It was found that the groove patterns have a significant effect on the result of the CMP, as well as the width and pitch of the groove. It was found that the groove patterns increase the NU of the sliding distance distribution. The circular-type groove caused the greater NU than the rectangular-type groove under the identical operating conditions. The optimized operating conditions were varied for different types of the groove patterns. The simulation method proposed in this paper may be further extended to analyze other process variables.