Abstract: A multibody system composed of free standing body and the basic platform is investigated by non-smooth dynamics of multibody system. Dynamic equations and numerical method of the system with non-smooth contacts are proposed. The free standing body consists of main body and supporting legs, which are connected by revolute joints with viscoelastic moments. The contact forces between free standing body and the basic platform are simplified as normal forces and frictional forces of contact points. Moreover, the modified Hertz contact model and Coulomb's law for dry friction are employed to describe normal forces and frictional forces, respectively. And the configuration coordinates of Cartesian coordinate system are used as the generalized coordinates. Firstly, the system's dynamic equations are established by Lagrange's equations of the first kind and the motion of basic platform is regarded as a rheonomous constraint. The problem of constraints violations is solved by Baumgarte stabilization method. Secondly, the numerical method of the multibody system are proposed, which is based on the event-driven schemes and linear complementarity formulations. The complementary formulations of friction saturations and the relative accelerations in the tangential are given, while the relative velocities in the tangential of the contact points are equal to zero. Therefore the judgements of stick-slip transitions for contact points and the solutions of frictional forces in stick situation could be solved as a linear complementarity problem. And the linear complementarity problem is solved by Lemke's algorithm. Finally, an appropriate step is chosen by the simulation. Then the numerical simulations denote the stick-slip phenomenon and the influence of basic platform as well as mass centre's position.