This paper presented a modeling and simulation method for the rigid multibody system with frictional translational joints and driving constraints. The geometric constraints of the translational joints were treated as bilateral scleronomic constraints and the driving constraints were rheonomic constraints. The frictional model of translational joint was characterized by the type of Coulomb's law. The dynamic equations were obtained by the Lagrange equation of the first type and the constraint equations of translational joints were given by distance function. The problem about the translations of the normal constraint forces acting on the sliders of translational joints was formulated and solved as a horizontal linear complementarity problem. The Baumgarte's stabilization method was used to decrease the constraint drift. Finally, a crank-rocker mechanism was considered as demonstrative application examples. The numerical results obtained show some dynamical behaviors of the system with frictional translational joints and constraint stabilization effect.