The problem of including flexibility of large manipulator system has not been satisfactorily resolved at this time for simulation and design. To simplify the analytical procedure to some realistic extent, this paper conceives a new mathematical treatment for dynamic analysis of large flexible manipulator systems. The essence of the idea is to separate the kinematics and flexibility analyses as two independent but successive steps in a small time interval. Superimposing the flexibility effect onto the kinematic result, the summation is viewed as the initial conditions of the next instant motion, and the dynamic analysis succeeds to the next time interval. Repeating this process, the kinematic analysis accompanying flexibility effect is accomplished for a required time period. Because an extremely complex analytical chore is resolved into two relatively simpler problems, the complexity of the dynamic analysis of large flexible manipulator systems is mathematically simplified. To demonstrate the applicability of the proposed methodology, an end-effector vibration suppression problem for a large manipulator system has been investigated.