Abstract: The theory and strategy of vibration control for flexible redundant manipulators are studied by the optimal control theory. The idea of active control is used to suppress vibration, and a method for suppressing vibration of flexible redundant manipulators is proposed. This method can increase the damping and the stiffness of the flexible redundant manipulator, and on the other hand eliminate the vibration exciting force by means of optimizing the self motions. Thus, the manipulator can use these self motions to quicken the consumption of its vibrational energy while tracing a required trajectory, so as to suppress vibration quickly. Furthermore, by analyzing the selection of the self motions which meet the need of suppressing vibration, it is found that flexible redundant manipulators still have the second optimization capability at the time of suppressing vibration through optimizing the self motions. And this second optimization capability can be used to optimize other objectives on the basis of suppressing vibration, which is very important for flexible redundant manipulators to improve their operational performance. Finally, with this method, some simulations are carried out, and the results demonstrate its feasibility.