A floating chuck mechanism provided at a workhead that is arranged at a processing apparatus for sandwiching a cylindrical-shaped workpiece by means of two center members along a rotational axis, the floating chuck mechanism causing the workpiece to rotate about the rotational axis and correcting an eccentricity between the rotational axis and a center of an outer diameter of the workpiece, includes a chuck body portion including plurality of clamp jaws for holding the workpiece from the outer peripheral side thereof, and a chuck base portion fixed to the workhead so as to rotate therewith, the chuck base portion including a fixed portion fixed to the workhead and a slide portion slidable along a slide surface perpendicular to the rotational axis. The chuck body portion is fixed to the slide portion and sliding along the slide surface so as to correct the eccentricity.