Vehicle ride quality is essential for ensuring the comfort of passengers and the protection of sensitive cargo. The vehicle dynamic state can be modelled as a complex few-DOF dynamical system. A vehicle having basic suspension and cargo platform (or damped panel) is considered here. The car body and the additional damper panel above the body are modelled by rectilinear rigid plates in the form of a parallelepiped. Equations of motion are described by the 10 DOF nonlinear system connecting vertical displacements, angles of rotation of each rigid plate, and vertical displacements of the unsprung masses. The fundamental vibration modes and natural frequencies at insignificant ver tical displacements and rotation angles are obtained. At sufficiently large displacements, under external periodic load, nonlinear forced vibrations are constructed numerically. A suspension system is analyzed that uses the integration of nonlinear and quasi-zero stiffness elements formed by a sinusoidal beam, a pair of semicircular arches and sufficiently rigid wall elements. Numerical and experimental studies confirm the efficiency of this system in the presence of dynamic loads acting on the vehicle.