Multibody dynamics is applied to the vibration analysis of mass-spring system which consists of a car body, suspensions and wheels. When an automobile is running on uneven terrain, displacement of the wheel is determined by contact condition between the wheel and the road. In this paper, rigorous and approximate constraint condition is presented in order to study kinematics of a rolling wheel on a plane curve. It is shown that approximate method is not able to predict the accurate motion when the curvature of the road is not negligible compared with that of the wheel. Analysis of the strut suspension model with rigorous method shows an irregular nonlinear oscillation under the ideal case of no damping.