Abstract: A method for modeling and simulation of longitudinal vehicle dynamics is presented based on non-smooth dynamics of multibody systems in this paper. The vehicle is the multi-rigid-body system which consists of a vehicle body, wheels and transmission system. It is assumed that wheels are linked with the vehicle body by shock absorbers and the transmission system is treated as the disk connecting with driving wheels by spring-damper system. The friction and the rolling resistance between wheels and the road are taken into account and the Coulomb's friction law is used to describe the frictional forces. Firstly, the lateral and bilateral constraint equations of the system are given in generalized coordinates of the system and the dynamical equations of the system are obtained by Lagrange's equations of the first kind. Secondly, the complementary formulations of friction law, rolling resistance law and contact law between wheels and road are given in order to determine state transitions from contact to separation and sticking to slipping. Based on the event-driven scheme, the problem of state transitions is formulated and solved as a horizontal linear complementarity problem (HLCP). The algorithm for solving these non-smooth DAEs is presented. The Baumgarte stabilization method is used to reduce the constraint drift. Finally, the multibody system of a vehicle is considered as an illustrative application example to analyse its dynamical behaviour affected by the engine output torque, the friction coeffcient and the rolling resistance coeffcient between wheels and road. The numerical results show that the phenomenon of the stick-slip between driving wheel and road occurs continually when the coeffcients have special values.