Abstract: The sleeve comprises two tubular rigid strength members (4,5) where one surrounds the other and where they are united by an elastomer body (6) shaped so as to co-operate therewith to form two sealed cavities (7,8) that communicate with each other via a narrow channel (9), the cavities and the channel being completely filled in a liquid, the portion of the elastomer body that defines at least one of the cavities having a generally U-shaped or V-shaped axial section that is outwardly open in a radial direction, and the narrow channel extending along an arc of a circle disposed at an axial end of the sleeve, close to its outer strength member (5). The outer strength member forms an integral portion of a rigid connection arm (11), and the narrow channel is defined in part by a radial flange (16) of a cage (15) received in the outer strength member.