Elastic damping element for damping vibrations of a line, comprising: an elastic sleeve ring for enclosing the line, wherein the elastic sleeve ring comprises an inner wall facing the line, which encloses a sleeve ring interior space for receiving the line, wherein a plurality of radially extending recesses (105, 105-1, 105-2) are formed in the inner wall, wherein a curved and tapered web extending in the direction of the sleeve ring interior space is formed between two recesses (105, 105-1, 105-2) formed next to each other in the inner wall, wherein the elastic sleeve ring comprises an outer wall facing away from the line, wherein a fastening element is arranged at the outer wall, which fastening element extends radially from the outer wall and is adapted to connect the elastic damping element to an additional component in a pluggable manner, wherein the fastening element comprises a fastening shaft, which is connected to the outer wall of the elastic sleeve ring and which extends from the outer wall in the direction of the additional component and is adapted to be passed through a fastening opening of the additional component, and wherein at least one fastening projection is arranged at the fastening shaft, which at least one fastening projection is adapted to abut at a side of the additional component facing away from the elastic damping element in order to ensure an effective attachment of the fastening element to the additional component, wherein the outer wall of the elastic sleeve ring comprises a contact surface facing the additional component, wherein a contact element is arranged at the contact surface, which contact element is adapted to abut at a wall of the additional component facing the elastic sleeve ring, and wherein the elastic sleeve ring of the elastic damping element is formed as a sleeve ring closed in the circumferential direction of the elastic sleeve ring or as a sleeve ring closable in the circumferential direction of the elastic sleeve ring. an elastic sleeve ring for enclosing the line, wherein the elastic sleeve ring comprises an inner wall facing the line, which encloses a sleeve ring interior space for receiving the line, wherein a plurality of radially extending recesses (105, 105-1, 105-2) are formed in the inner wall, wherein a curved and tapered web extending in the direction of the sleeve ring interior space is formed between two recesses (105, 105-1, 105-2) formed next to each other in the inner wall, wherein the elastic sleeve ring comprises an outer wall facing away from the line, wherein a fastening element is arranged at the outer wall, which fastening element extends radially from the outer wall and is adapted to connect the elastic damping element to an additional component in a pluggable manner, wherein the fastening element comprises a fastening shaft, which is connected to the outer wall of the elastic sleeve ring and which extends from the outer wall in the direction of the additional component and is adapted to be passed through a fastening opening of the additional component, and wherein at least one fastening projection is arranged at the fastening shaft, which at least one fastening projection is adapted to abut at a side of the additional component facing away from the elastic damping element in order to ensure an effective attachment of the fastening element to the additional component, wherein the outer wall of the elastic sleeve ring comprises a contact surface facing the additional component, wherein a contact element is arranged at the contact surface, which contact element is adapted to abut at a wall of the additional component facing the elastic sleeve ring, and wherein the elastic sleeve ring of the elastic damping element is formed as a sleeve ring closed in the circumferential direction of the elastic sleeve ring or as a sleeve ring closable in the circumferential direction of the elastic sleeve ring.