Abstract: The invention relates to a shock and/or vibration damping device comprising a body adapted to be assembled to a supporting element, a concavity provided in the body in which is introduced a piston whose rod is adapted to be assembled to a supported element, and at least one resiliently deformable supporting membrane arranged in the cavity and interposed between the head of the piston and the cavity bottom wall. This membrane is mounted freely slidable at its periphery within the cavity and comprises in proximity to its periphery a stiffening element at least partially embedded in its mass. The head of the piston is advantageously embedded in the mass of another membrane which may be identical with the supporting membrane, the tops of the two membranes bearing against one another and wherein the shape of the surface of one of the membranes is at least partially conformed to the shape of the confronting surface of the other membrane.