To provide a supporting device for an elastic roller that supports the outer periphery of a rotary shaft, allows finishing at an accuracy higher than the vibration accuracy of the rotary shaft itself, and can apply only a driving force to one end of the rotary shaft even in a workpiece susceptible to bending or twisting, when the outer peripheral surface of the workpiece having an elastic body layer on the outer periphery of the long rotary shaft is precisely polished.

A parallel pin 2 to be attached to a collet chuck A on the spindle side is fixed to one end of a universal joint 1 for transmitting only the driving force to the rotary shaft W1, a clutch holder 3 having a one-way clutch 4 mounted to its inner periphery is fixed to the other end, a gripper 5 for gripping and fixing the clutch holder 3 and a bearing bracket 7 having an outer peripheral support material for supporting the outer periphery of the rotary shaft W1 are fixed to a fulcrum 8, and an outer peripheral support material on the core pressing pedestal side for supporting the outer periphery of the rotary shaft W1 is built in a center 9 on the core pressing pedestal side.