An attachment device (2) for use in the vacuum therapy of wounds has a vacuum-tight mounting element (6). A conduit is fastening to the upper side of that mounting element in a vacuum-tight manner. The conduit (4) communicates with the wound space through openings (22) in the mounting element (6) and in the vacuum dressing. The conduit (4) is flexible and flat and is connected to the mounting element (6) non-detachably and extensively in a longitudinal section (8) on the wound side over at least 70% of its surface projected perpendicularly onto the mounting means (6). The conduit (4) is made out of a flexible elastomer material of Shore A hardness of no more than 60 and the thickness (D) of the combined conduit (4) and mounting element (6) is no more than 7 mm.