This paper addresses a design method of robust tracking control systems of flexible arms using inverse dynamics. The controller is constructed having two independent feedforward and feedback controllers. The feedforward controller has been designed considering the inverse dynamics of the flexible arm system. Since the flexible arm system has non-minimum phase characteristics, the inverse dynamics has been divided into causal(stable) and anticausal(unstable) parts and has been solved in time domain to obtain the feedforward control input. In order to provide stability robustness against unmodelled dynamics and performance robustness against frictions forces on the bearings, the feedback controller has been designed on the frame work of H∞ control theory. The dynamics model of the flexible arm system has been formulated using distributed parameter system method and the validity of the model has been experimentally verified. The simulation results of the control system have been demonstrated.