This paper presents the formulation of developed second order sensitivity analysis when applied to shape optimization in design of electrical machine problems. It used the second order sensitivity analysis based on numerical approach that is variable have mixed solution limits to the shape optimization problems which using with standard electromagnetic design analysis (EDA) software. Based on this numerical methodology; designers will be able to deal with practical design optimization of electrical machines using with standard EDA software. The applicability of the proposed methodology is demonstrated by optimizing the salient pole synchronous hydro generator. The results show that the sensitivity analysis technique is provided improvement of solution about %15 and would appear to have certain important advantages over the other methods.