For high performance rotating machinery, unstable vibrations may occur caused by hydrodynamic forces such as oil film forces, clearance excitation forces generated by the working fluid, and etc. In order to improve the availability one has to take into account the vibrations very accurately. When designing a rotating machinery, the stability behavior and the resonance response can be obtained by calculation of the complex eigenvalues. A suitable modifications of seal and/or bearing design may effectively improve the stability and the response of a rotor system. This paper deals with the optimum length and clearance of seals and bearings to minimize the resonance response(Q factor) and to maximize the logarithmic decrement in the operating speed under the constraints of design variables. Also, for an avoidance of resonance region from the operating speed, an optimization technique has been used to yield the critical speeds as far from the operating speed as possible. The optimization method is used by the genetic algorithm, which is a search algorithm based on the mechanics of natural selection and natural genetics. The results show that the optimum design of seals and bearings can significantly improve the resonance and the stability of the pump rotor system.