This paper presented a numerical algorithm for solving the dynamic equations of singledegree offreedom multibody system with bilateral constraint and single frictional point,and the generalized dynamic equation of the systems was derived. Because the dynamical equation was strongly nonsmooth and nonlinear ODE, the dynamical behavior of the system cannot be studied by using the conventional methods for smooth systems. Therefore, a simple algorithm was presented by utilizing the characteristics of equation and physical meaning of variable. The efficiency and the precision of our algorithm were higher than the iterative ones.