A vibration damper includes a cylinder to which a clamp-shaped attachment part is fastened, wherein the attachment part has a tubular body which contacts an outer lateral surface of the cylinder and has at both ends thereof radial tabs which are spaced apart in circumferential direction and by which a pre-loading in circumferential direction is introduced in the tubular body by clamping devices, wherein the tubular body has an elongation portion oriented in circumferential direction of the lateral surface of the cylinder.