This paper presents a new assist control method for positioning tasks using a master-slave manipulators with the elasticity on the slave arm. This manipulator is called a flexible master-slave manipulator (FMSM). When the operator performs the positioning task using the FMSM, the remote operation becomes too difficult owing to the elastic vibration of the slave arm. In order to reduce the operator's load, we design a new assist control method. Then by introducing strain feedbacks to the conventional (force reflecting servo type) bilateral control, (i) an autonomic vibration control and its switching control are added to the slave controller, and (ii) a force feedback depending on the elastic vibration to an operator is added to the master controller. We examine the stability of the closed-loop system with the human model and the proposed control system. And we evaluate the maneuverability and the operation feeling of the proposed assist control method on the basis of the task success time and using the SD method and the principle component analysis. These evaluation results show the improvements of the maneuverability and the operation feeling and confirm the effectiveness of the proposed assist control method.