A clamping device for clamping a flexible packing (2, 3) of a cylinder (1) of a printing press, which cylinder has an axial channel (6) on a jacket surface, the clamping device includes a clamping body (10), which has a surface (S) that forms in the channel (6) with an opposite surface (4) a clamping gap for at least one end of the packing (2, 3) protruding through an opening (7) of the channel (6). A pressing device (13; 14; 10a) presses the clamping body (10) and the opposite surface (4) against each other with a clamping force (F). A mounting device (12; 14; 1, 8), which forms a support surface (9; 14′; 9′), touches the clamping body (10) and the clamping body (10) is supported on it. A center of gravity (SP) of the clamping body (10) can be moved, while the clamping gap is maintained, at right angles to an axis of rotation (DZ) of the cylinder (1) in a first direction relative to the cylinder (1) and the support surface (9; 14′; 9′) and in a second direction that is not parallel to the first direction in relation to the cylinder (1).