The paper presents the results obtained from simulating the behavior of a car with a rigid rear axle and anti-roll bar. The four-degree-of-freedom model presented allows the analysis of coupled bounce-sway vibrations for a passenger car with a rigid rear axle and anti-roll bar. For separate excitations at the wheels, the equations of motion are determined by applying the center of mass motion theorem and the moment momentum theorem. These, put into matrix form, lead to the obtaining of inertia, viscous damping and stiffness matrices. The presented equations also include the forces introduced by the anti-roll bar, an element considered to have a linear elastic behavior. Greater attention is paid to the contact between the wheel and the road, as it is known that anti-roll bars improve the comfort of a vehicle. Based on the mathematical model determined, a numerical model is obtained, using MATLAB program, on the basis of which various simulations are made, for the study of the influence of the vehicle’s speed, for the study of the influence of the damping coefficient of the shock absorbers and for the study of the influence of the anti-roll bar stiffness value on the dynamic behavior of the vehicle. The results are presented in the form of diagrams and tables with determined values. At the end of the paper, the conclusions and directions of interest of the authors are presented.