An apparatus support (11) with a damping characteristic comprises a rigid reinforcing component, in particular a steel plate (19), encapsulated by a body (16) of compliant material, particularly a composite of particulate mineral material and synthetic binder. The plate (19) defines an opening (19a) at spacing from the upper side of the body (16) and a mounting ring (21) is embedded in the body so as to be disposed at least partly above the opening. The ring (21) has a peripheral flange (21a) which is spaced from the plate (19) and from the upper side of the body and overlaps the plate in vertical projection. Material of the body is thus disposed above the flange (21a) and also sandwiched between the flange and the plate so that a damping zone is present around the ring both above and below the flange.