A power damping mechanism for an input shaft of an auxiliary machine of an engine that is configured to be driven by the engine via a power transmission mechanism is provided. The power damping mechanism comprises a retainer plate that is fastened to the input shaft of the auxiliary machine and is rotatable with the input shaft, the retainer plate having a plurality of tubular retainer portions arranged to be equally spaced apart from each other in a circumferential direction; a damping member having a damping portion that is fitted to each of the retainer portions and is made of an elastic material, and a fastening portion by which the damping portion is fastened to the power transmission mechanism. The input shaft of the auxiliary machine is coupled to the power transmission mechanism via the damping member and is configured to operate in association with the power transmission mechanism.