A method for dynamics modeling and numerical algorithm of multibody system with friction and MovingbilateralSlot was provided.At first,the dynamic equations of the system were derived from the first kind of Lagrange’s equations by using the Cartesian coordinates and local approach of constraint equations.A onetoone correspondence between the constraint forces of the system and the Lagrange multipliers was established to analyze and compute the friction forces conveniently.Secondly,with the augmentation approach,the differentialalgebraic equations were transformed into ordinary differential equations of partitioned matrix form,which can improve the calculating efficiency.Finally,a numerical example was given to prove the method to be effective.