The present investigation studies the lateral stability of vehicles by using a two-degree-of-freedom bicycle model which is implemented based on MATLAB/Simulink. The proposed model considered the driver model as an expert system to mitigate the vehicle's lateral deviation. Rear-wheel steering is incorporated into the typical front-steering vehicle model to represent a Four-Wheel Steering (4WS) system that improves lateral vehicle stability. The linear optimal control theory (LQR) is employed to determine the rear wheel steering angle as the control action to minimize the vehicle lateral responses of the vehicle, such as body sideslip angle, lateral deviation, lateral acceleration, and yaw rate. To validate the effectiveness of the proposed controller, the Particle Swarm Optimization (PSO) algorithm is designed to obtain the optimal gain of the LQR. Three scenarios are utilized to evaluate the proposed model. First, at a lateral deviation of 2.5 m; second, at a front steering wheel angle of 4 degrees; and third, activating both previous scenarios together. The vehicular lateral responses are represented in the time domain and root mean square values. Significant improvements are observed in the lateral stability of the vehicle whereas active four-wheel steering is employed, particularly in terms of lateral acceleration, lateral deviation and yaw rate compared to the typical 2WS vehicle.