In this paper, iterative learning control technique is applied for the first time to a class of flexible systems. Specifically, learning control of a material transport system is considered. The system consists of a stretched string and a transporter. The motion of transporter is subject to such external disturbances as imperfect wheels and can cause string vibrations. The control objective is to damp out any string oscillation during transportation using iterative control applied at the boundaries. The control is designed using both discrete and continuous time Lyapunov functions. The proposed result is new and significant as it demonstrates that iterative learning control methodology is an effective technique for controlling distributed parameter systems.