In this paper issues related to the vibration suppression in the drive system with an elastic joint are presented. The cascade control structure with two additional feedbacks from the shaft torque and the difference between speeds which allows the free location of the system closed-loop poles is considered. The influence of the system poles to the drive performance is shown. Then the control structure with additional feedbacks from the load torque and its derivatives, which allow rejection from the load speed the fall caused by the load torque change, is introduced and examined. To provide the information of non-measurable state variables the Extended Kalman Filter is used. The effectiveness of the proposed structure has been examined under simulation and experimental study.