The presence of flexibilities in rotational joints can limit the kinematic performances of manipulators doing high speed tasks as Pick and Place. The problem addressed in this work concerns the vibration control of serial robots with flexible joints performing Pick and Place tasks in order to improve productivity. Based on a dynamic model of a robot with flexible joints, a model-based control law is proposed with its associated tuning methodology. The robot dynamic model is then the key point of our methodology. This dynamic model considers stiffness and damping of each flexible joint. To guarantee its accuracy, a geometrical and dynamic identification procedure is realized. The objective is to show the relevancy of the proposed approach which integrates joint flexibilities in the control law. Theoretical results based on a representative model are used to illustrate the benefit of this model-based control law compare to two other control strategies (Feedforward control and control dedicated to rigid structures). Finally, a sensitivity analysis of this control law is realized to quantify the impact of modelling error and conclude on the criticality of joint damping value on vibration decreasing.