Abstract: In this paper, the bracket of a electric equipment is designed by considering the vibration and shock environment. According to the design requirement with respect to vibration and shock, the stiffness of the isolator is used as the design variable. The mathematical optimal model for searching the largest stiffness of isolator is built to make the relative displacement small. The optimal problem is solved using ANSYS. Both the mode superposition method and the Newmark integrating method are used to obtain the response of stochastic vibration and shock. The optimal results could be used in the isolator design of the electric system.