To achieve the performance of mechanisms and machines to a higtlet accuracy, the elastic deformations of their members, under dynamic conditions, are to be taken into account. In the presented work each member in the link-age is treated as being elastic. The kinematic equations of constraints at the kinematic pairs are presneted. These equations are introduced into the equations of motion through Lagrange multipliers, to obtain a coupled system of nonlinear algebric and differential equations. The later system will have the same form for each element. So, the total set of equations, describing the linkage, can be generated automatically. Illustrative examples are given and the agreement of the results with those previously solved using other techniques is satisfactory.