This paper deals with the modelling and control of differential steering for vehicular motions with the help of Sliding Mode Control (SMC) with a Super-Twisting Algorithm (STA). A single-track mechanical model of the vehicular dynamics is proposed and validated by simulations. A control strategy based on the STA is proposed for the yaw dynamics to improve travel comfort and the stability of the vehicular motion. The desired yaw trajectory is given and the equivalent and corrective control parts of the STA are calculated by the controller. Simulation results show the effectiveness of the proposed control strategy.