A pressing device (1) for pressing finishing tape against circumferential surfaces (2) of substantially cylindrical work piece sections (3) in a finishing process includes at least one elastically bendable pressing element (5) that is substantially inelastic in the longitudinal direction. A support element (6) has two bearings (7), which are arranged at a distance from each other. The pressing element (5) is fastened to the two bearings, and the two bearings are arranged in such a manner that finishing tape is pressed against a circumferential surface (2) by the pressing element (5) across a contact angle (4) using a pressing force. The pressing device (1) is adjustable in order to process work piece sections (3) of different diameters. The pressing element may be a toothed belt (5) having tooth-like ribs (8), and the toothed belt (5) is interlockingly mounted in the support element (6) using the tooth-like ribs (8).