Abstract: The problems of trajectory tracking control and vibration suppression of a rigid flexible manipulator are discussed. The nonlinear dynamic equation of a two-link rigid flexible manipulator is established. The nonlinear decoupling feedback control method based on the model is used to partly decouple the joint variables and elastic deformation. The inverse dynamic method of manipulator and the Linear Quadrics (LQ) optimum control method are employed to investigate the problems of trajectory tracking and eliminating the remaining vibration. It is demonstrated by numerical simulation that the proposed methods are efficient.