This paper presents a computational method for obtaining an optimal control trajectory for point-to-point motion of a cooperating robot carrying a flexible object. To increase the overall productivity and its efficiency, it is required to move the object as fast as possible using the maximum capacity of actuators of robots. If the carrying object is very sensitive to vibration, the robots should be operated so as not to cause excessive vibration of that object. This work deals with optimal input design for cooperative robots to reduce vibration of flexible objects that are handled at speed, under firm constraints on control torques.