This paper presented a method for modeling and simulating planar rigid multibody systems with nonsmooth revolute joints. The geometric constraints of the revolute joints were treated as bilateral constraints, and the tiny clearance sizes were neglected. The LuGre friction model was used to describe the tangential contact forces in the revolute joints. The dynamic equations (differentialalgebraic equations) were obtained by using Lagrange′s equations of the first kind. Due to the frictional forces in the revolute joints, the dynamic equations are nonlinear algebraic equations with respect to the Lagrange multipliers. Because of the perfect continuity of the LuGre friction model, numerical algorithms for nonlinear algebraic equations and differential equations,such as QuasiNewton method and RungeKutta method, were combined to solve the dynamic equations. Finally, the feasibility and effectiveness of the method were verified by numerical examples, which showed that the method can consider the frictions in revolute joints, and at the same time also avoid the numerical difficulties caused by Coulomb dry friction model.