In a mechanical structure development focusing on the noise and vibration, numerical analysis method like finite element method and structural optimization is widely used to predict and improve a frequency response of the structure. But, the results of these method are idealized and uncertainties in structure like parts shape and connecting part are neglected in many cases. In recent years, the mechanical structure is becoming slim and light weight to save a energy. Therefore, the influence of the uncertainties becomes large relatively, so it is necessary to take in the uncertainties to the numerical analysis. In this paper, as a one of the numerical analysis with uncertainties, robust design method based on stochastic finite element method and structural optimization will be discussed to minimize frequency response variance of structure by the uncertainties. In this paper, the robust design method were explained in detail. And, as an example of application, the robust design method was applied to an FE model. It showed that the structure which minimize the frequency response variance can be find efficiently by the robust design method.