In this paper, analysis of a half-car model with linear and nonlinear semi-active dampers is performed. Using Matlab-Simulink software, a response of the system to a harmonic excitation of variable frequency and to an impulse excitation is found. The effect of both the distribution of spring-supported mass and the asymmetry of the support on the frequency characteristics of velocities and displacements at the mounting points of the dampers are analyzed. Additionally, characteristics of forces generated by the semi-active dampers and the response of the system when crossing an obstacle are determined.