The contact mechanism should be analyzed for an estimation of the performance of a traveling wave ultra-sonic motor (TWUSM), because the operation of this type of motor depends on the frictional force between the rotor and the stator. However, the nonlinearity of the contact mechanism of the TWUSM makes it difficult to proposed a proper contact model, a characteristic analysis method and an optimal design method. To address these problems, a characteristic analysis and optimal design method using a cylindrical dynamic contact model (CDCM), an analytical method, a numerical method and an evolutionary strategy algorithm (ESA) is proposed in this research. The feasibility and usefulness of the proposed characteristic analysis and optimal design method are verified through experimental data. Furthermore, the importance of the shape of the teeth and the reason for the improvement of motor performances by the chamfering at the teeth are proposed and verified in this paper.