Device for the shock-absorbing attachment of two elements ( 2, 3) to be assembled, the attachment device comprising: - an inner part that is tubular along an axis of attachment intended to be rigidly attached to an element to be assembled, and comprising an outer lateral surface; - an outer part that is tubular along the axis of attachment, and is hollow, intended to be rigidly attached to another element to be assembled and comprising an inner lateral surface, the inner part being accommodated in the outer part so that the outer surface of the inner part is facing the inner surface of the outer part; - an elastomer layer between the outer part and the inner part, the attachment device being characterized in that the outer lateral surface of the inner part comprises at least one irregular portion and the inner lateral surface of the outer part comprises at least one irregular portion complementary to the irregular portion of the outer surface of the inner part, the elastomer layer comprising a first face bonded to the irregular portion of the lateral outer surface of the inner part, and a second face opposite to the first face, bonded to the irregular portion of the lateral inner surface of the outer part, and in that the elastomer layer, when viewed in cross-section in a longitudinal plane comprising the axis of attachment, comprises: - on each side of the axis of attachment, at least three portions ( 28a, 28b, 38a, 38b, 29a, 29b), called longitudinal, distributed in the direction of the axis of attachment with a predetermined pitch, at least one of the three longitudinal portions ( 28a, 28b, 38a, 38b, 29a, 29b) working against the other two portions in the direction of the longitudinal axis and - at least two portions ( 27a, 27b, 37a, 37b, 29a, 29b), called transverse, working in a direction that is transverse to the axis of attachment, a first portion ( 27a, 29a, 37a) being situated on a first side of the axis of attachment and the second portion ( 27b, 29b, 37b) being situated on the other side of the axis of attachment. - an inner part that is tubular along an axis of attachment intended to be rigidly attached to an element to be assembled, and comprising an outer lateral surface; - an outer part that is tubular along the axis of attachment, and is hollow, intended to be rigidly attached to another element to be assembled and comprising an inner lateral surface, the inner part being accommodated in the outer part so that the outer surface of the inner part is facing the inner surface of the outer part; - an elastomer layer between the outer part and the inner part, - on each side of the axis of attachment, at least three portions ( 28a, 28b, 38a, 38b, 29a, 29b), called longitudinal, distributed in the direction of the axis of attachment with a predetermined pitch, at least one of the three longitudinal portions ( 28a, 28b, 38a, 38b, 29a, 29b) working against the other two portions in the direction of the longitudinal axis and - at least two portions ( 27a, 27b, 37a, 37b, 29a, 29b), called transverse, working in a direction that is transverse to the axis of attachment, a first portion ( 27a, 29a, 37a) being situated on a first side of the axis of attachment and the second portion ( 27b, 29b, 37b) being situated on the other side of the axis of attachment.