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In the field of industrial machines, the mechanical systems composed of the power circulation structure exist, and the powers of two or more motors of the same output are synthesized through the gear stages to drive the driven machine part and the desired motion of the machine is achieved. In this paper, the case that the power circulation mechanism is driven by two motors is taken up. First, the analytical model for the torsional vibration and the analytical result are shown. Second, the stability of the control system is considered by calculating the loci of system eigenvalues. Third, the suppression effects on the residual vibration generated in the driven machine part when motors start and stop by applying the model-based control concerning the velocity control loop is confirmed by the simulation. Simulations show satisfactory control results to reduce the transient vibration at the driven machine part.