A polymeric material having a shielding effect against radiation is provided in the form of a shaped body which may be a plate, flexible sheet, or of any other desired shape, which body consists essentially of a synthetic plastic material including synthetic rubber, or of natural rubber, having distributed therethrough and intimately mixed therewith an effective amount of at least one compound of a saturated fatty acid being solid at room temperature and having at least 9 carbon atoms with at least one metal selected from the group consisting of lead, bismuth, tungsten, zirconium, iron, tin, cadmium, lithium and barium.