In this study, the natural frequencies, body displacements, velocities, and accelerations of a quarter-car with double wishbone suspension are examined by considering the proportionally damped system. Two models of quarter-car suspension system are idealized employing two different assumptions due to the suspension links to describe the dynamic behaviour of vehicles running on base excitation. In the first model, the links of the suspension are assumed to be rigid and the stiffness and mass matrices of the model are obtained by using the analytical method. In the second model, the links of the suspension are assumed to be flexible and the elastic stiffness, mass, and geometric stiffness matrices are obtained by using Finite Element Method. In order to express the linear equation of motion, suspension link forces required for the geometric stiffness matrices are assumed as constant. Also, the oscillations of the suspension links are neglected since the base displacement is chosen in small amplitude. Two Matlab programs regarding the aforementioned models have been developed. Firstly, the natural frequencies of the models are found. Then, the displacements, velocities, and acceleration of the car body are presented in graphical forms for the specified car speed. The excellent agreement between results of the analytical model and finite element model is observed for both natural frequencies and the time reponses. The effect of loads on suspension link on the dynamic behaviour of suspension system is also studied.