PURPOSE: To prevent the wear of the driven side fitting yoke of the coupling supporting device between the driving shaft and rolling roll of a rolling mill by constituting the rollers of the above-mentioned yoke in such a manner that the rollers can be axially moved.

CONSTITUTION: The driven side fitting yoke 37 of the coupling which interposes a splined shaft joint 6 between the driving side and driven side fitting yokes 31 and 37 and connect the two yokes by means of universal joints 32 and 36 is freely rotatably supported by a pair of the rollers 54 and is so provided that the driven side fitting yoke 37 can move to follow up the extension and contraction of the splined shaft joint 6. In addition, the wear of the driven side fitting yoke 37 is prevented by energizing the same toward the splined shaft joint side.