This paper shows the possibility of creating a suspension of a car with a nonlinear elastic characteristic based on a four-link lever mechanism. It also presents the kinematics and dynamics of the mechanical suspension system. As a result of the study, the kinematic laws and distribution of forces in the nodes of the suspension have been found. The dependence of general rigidity on the stiffness of the main and additional elastic elements have been determined for obtaining the required nonlinear elastic characteristic. An example of a given nonlinear elastic characteristic is presented.