In this paper, a modeling and simulating method is presented for the planar rigid multi-body system with friction-affected translational joints. The dynamical equations of the non-smooth system are formulated by the first kind of Lagrange's equations in Cartesian coordinate system. The normal forces are expressed by the Lagrange multipliers, and the frictional forces are characterized by Coulomb's friction law. The state transition problem of stick-slip and normal forces of bilateral constraints is solved by an improved trial-and-error method. Finally, the planar rigid multi-body system with two translational joints is considered as a illustrative application example.