The invention relates to an annular clamping element (10) with an annular housing (21), which has at least one pneumatic or hydraulic connection (13), and a ring piston (91), which can be moved in two stroke directions in the longitudinal direction of the annular clamping element. The housing has a rigid cylinder casing region (62) that surrounds a longitudinal axis oriented in the longitudinal direction and which comprises a guide section (63) and a free-standing inner wall (61), which has at least two clamping contact plates (73). Each clamping contact plate has a rolling surface (76) on the exterior. The inner wall, the ring piston, and at least two rolling bodies (131), each of which is mounted between an individual rolling surface and the ring piston, form a splined transmission, the frame of which is the cylinder casing region. During a movement of the ring piston, said movement being guided along the guide section, in one of the stroke directions of the ring piston, the inner wall is deformed radially to the longitudinal axis in the region of the clamping contact plates against an internal restoring force of the inner wall. The invention provides an annular clamping element with a long service life which can be used for braking and/or fixing purposes.