This paper presents a mathematical vehicle model that is designed to analyze the dynamic performance and to develop various safety control systems. Wheel slip controllers for ABS is also formulated to improve the vehicle response and to increase the safety on slippery road. Validation of the model and controller is performed by comparison with a commercial software package, CarSim. The result shows that performances of developed vehicle model are in good accordance with those of the CarSim on various driving conditions. Developed ABS controller is applied to the vehicle model and CarSim model, and it achieves good control performance. ABS controller improves lateral stability as well as longitudinal one when a vehicle is in turning maneuver on slippery road. A driver model is also designed to control steer angle of the vehicle model. It also shows good performance because the vehicle tracks the desired lane very well.