A tumbling machine (1) for finishing treatment of workpieces has a plurality of tumblers (2) with vibratory tubs (31) mounted upon a carousel support structure (3). One or more processing stations (4-9) face the carousel support structure, and intermittent drive means (60,62) are provided to advance the plurality of tumblers (2) upon the carousel structure (3) relative to the processing stations (4-9).