The paper presents a model of a car with special attention given to the drive system. Two possible drive systems were considered: with standard differential and independent drive of each wheel by means of an electric motor. In both cases, flexibilities of live axle shafts have been taken into consideration. A 3D model of the car was assumed. The model consists of a system of rigid bodies connected one with another by means of elastic-damping elements. The phases of static and kinetic friction were considered in the steering and drive systems. The method of homogenous transformations was used in the mathematical description. The results of computer simulations are presented.