Abstract: The study of vehicle contact dynamics contributes to a more comprehensive understanding of the mechanical performance of the entire vehicle, and has a guiding role in the design of vehicle stability and cabin comfort. Therefore, this article is based on the theory of non smooth multi body system to conduct contact dynamics research on vehicle systems. Taking into account that the tire is the only component in contact with the ground during the driving process of vehicle, the tire dynamics model plays a crucial role in the overall vehicle dynamics analysis. First of all, this article establishes a multi body dynamic model of tires based on absolute coordinate modeling method. Then, by means of the Lagrange multiplier method, the constraint equation is introduced into the Lagrange function, and based on the second type of Lagrange equation, the general dynamic equation of the entire vehicle system is derived. Due to the presence of contact collisions, the state variables of the vehicle may exhibit discontinuity. In this paper, the Newton impact law is used to establish a non smooth mathematical formulation for impact response, and the smoothed Fischer-Burmeister function is used to equivalently replace the non smooth mathematical formulation to improve computational efficiency. Secondly, this article transforms the solution of friction response into an optimization problem for description, in order to avoid singularity when solving the friction direction. In addition, the general dynamic model of the vehicle system is decomposed into smooth and non smooth parts, and a detailed solution process is given based on generalized-α method. In the end, numerical simulations of contact collisions under multiple operating conditions are conducted on the entire vehicle system, and the impact of contact response under different operating conditions on the vehicle's dynamic performance is analyzed, and verified the effectiveness of the method proposed in this article.