Abstract: In the dynamic equations of multi-body system derivated by the first kind of Lagrange’s equa¬tions, the idealized constraint forces can be expressed as functions of the Lagrange multipliers. An approach to solve con¬straint forces of multi-body system is presented by means of Cartesian coordinate and partial ap¬proach of constraint equations. The normal constraint force of fixed surface and the projection of each joint reac¬tion force in inertia coordinate are related to Lagrange multipliers one-to-one, so that the constraint forces can be derived. A numerical example is used to demonstrate the effectiveness of this method.