In this paper the dynamic analysis of an electric vehicle (EV) has been investigated. The vehicle suspension system was built using multi-body dynamics (MBD) software, Altair MotionView/MotionSolve. Using the model, the dynamic properties of a target vehicle with gasoline engine and an electric vehicle with motor and batteries were simulated. The kinematic simulation of the suspension system was also carried out to analyze their kinematic performance. This paper mainly focuses on the lateral acceleration, roll angle and yaw rate characteristic of the vehicle in step steer analysis. By using optimization software, Altair Hyperstudy, parameterized models of the front and rear suspension were assembled. Then the optimization of dynamic properties of the electric vehicle suspension system was carried out.