Abstract: The invention relates to a polishing drum (1) which is intended particularly for polishing the edge surfaces and outer surfaces of straight and curved workpieces (101) and which carries an abrasive sheet (70) on a center cylinder (2) and is intended to be driven for rotation by a drive means (100). The polishing drum includes an elastic sleeve (60) or cloth which can be tensioned around the cylinder (2) and which forms an underlying supportive surface for the abrasive sheet (70). The center cylinder (2) has an axially extending slot (6) and means (40, 61) for tensioning the elastic sleeve (60) or cloth and the abrasive sheet (70) are provided inwardly of the slot (6).