In a conventional vehicle, the longitudinal shocks caused by the road obstacles cannot be effectively absorbed due to the fact that the longitudinal connections between the chassis and wheels are typically very stiff compared with the vertical strut where the regular spring is mounted. To overcome this limitation, a concept design of a planar suspension system (PSS) is proposed. The rather stiff longitudinal linkages are replaced by a spring-damping strut in a PSS so that the vibration along any direction in the wheel plane can be effectively isolated. For a vehicle with such suspension systems, the wheels can move forth and back with respect to the chassis. The wheelbase and load distribution at the front and rear wheels can change as a consequence of the implementation of the PSS on a vehicle. The planar system can induce changes in the vehicle dynamic behavior. This paper presents the overview introduction of a dynamic study of a vehicle with such suspension systems. The simulation results are analyzed and compared with those of a similar conventional vehicle.