This paper describes the optimum damping conditions for transient vibrations of a rotor-shaft system supported by flexible bearing pedestals. The transient vibration of a rotor can be effectively reduced by optimizing the damping ratio of flexible pedestals. The optimal damping ratio corresponds to the maximum value of the logarithmic decrement of a rotor. It is shown that the optimum damping ratio for the transient response calculated by the root locus method is different from the optimum one for steady-state response obtained from the principle of a dynamic damper, and the difference between these optimum damping ratios can be minimized by adjusting the controller gains and / or the dynamic properties of pedestals. The analytical results are confirmed by the experiment for a rotor system supported by flexible pedestals with electromagnetic actuators.