In the design of modem rotating machinery, it is often necessary to increase the performance of rotor-bearing system. Since a critical speed range influences the performance and safety of the whole system, it should be necessary to constrain the critical speed and thus resonance response in design process to result in large vibration. Consequently the minimization of resonance response amplitudes within the operation range of the rotor system becomes the most primary design objective. In this paper, based on the assumption that the external shape of rotating-shaft, bearing supporting positions and etc, the natural frequency analysis of spindle is performed by ANSYS $10.0^{(R)}$ Optimum design is conducted using the RBF model.