In order to carry out a comparative study of the passive, semi-active and active suspension of a truck cabin, a dynamic half model of truck is developed in the Simulink Matlab module. Its objective is to determine the comfort of the passengers and the stability of the vehicle when running by determining the root mean square acceleration at the cabin floor and the angle of inclination in the longitudinal plane for cabin in each configurations of the suspension system. In the model, different road characteristics and different travel speeds can be implemented. Simulink allows the easy manipulation of different types of controllers, thus an adaptive control system is used for the active suspension, a proportional-integral-derivative controller, whose parameters are optimized by genetic algorithm. The results of the dynamic response obtained after the simulations confirm the major improvement in comfort in case of using the genetic algorithm. For the suspension of the chassis, two constructive variants were considered, a passive suspension and a semi-active suspension.