An antivibration/antishock device includes a support member and a supported member disposed face to face and joined by a plurality of cable segments disposed on opposite sides of the support and supported members. Each of the cable segments is fixed to the support member and to the supported member and extends between the support and supported members in an at least partly curved cable path. The support and supported members are also joined by at least two stabilizer blades also fixed at their ends on opposite sides of the support and supported members. The stabilizer blades have a profile substantially corresponding to that of the cable path of the cable segment.