Abstract: The modeling and numerical algorithm for a planar multi-body system with friction on revolute joints are developed. Based on the model of a revolute joint, the dynamic equations of the system are derived by the first kind of Lagrange’s equations, then the relationship between Lagrange multipliers and the normal constraint force acting on the joint is obtained and the generalized force of friction is given. For the equations are piecewise continuous nonlinear algebraic equations about Lagrange multipliers, Quasi-Newton and Runge-Kutta algorithms are used to simulate the dynamical systems during the continuous interval (the relative angular velocity of the body does not equal to zero), and Particle Swarm Optimization, the trial and error method and Runge-Kutta algorithm are applied to solve the equations at the discontinuity points (the relative angular velocity of the body equals to zero). This algorithm overcomes the difficulty of choosing the initial values of Lagrange multipliers at discontinuity points. A numerical example is provided to demonstrate the validity and feasibility of the method.