In this paper, sensitivity formula with analytical method is derived for calculating structural natural frequency, and the partial derivative of plate element stiffness matrix and mass matrix with respect to design variables are gained respectively. Computer programs for computing frequency sensitivity with analytical method are developed. And combining it with large finite element structural analysis software ADINA, the optimal design software based on genetic algorithms, a structural dynamic optimization program system is constituted for computing structural natural frequency sensitivity with analytical method. Finally, the program system is applied to the optimal design of a turbine scroll case of a hydropower station (taking into account the natural frequency constraints). Calculation results show that analytical method presented in the paper is of higher computational precision, good stability, convenient to use, and can be popularized. Calculation results obtained the approval of client and used in real engineering.