A shaped article comprising at least a core element having generally flat top and bottom surfaces, the core element being made of elastic polymer and preferably reinforced. Presently preferred forms of the article are those in which the core element has a covering element secured to one or, in some cases, to both flat surfaces and providing an outer surface of an open-pore tissue-ingrowth-receptive material. Another preferred form of the prosthesis comprises a curved, flat, bar-like element shaped into a spiral configuration, so that the overall appearance approximates a flat disc. Still another version includes a plurality of flexible, curved, bar-like elements with configurations which allow them to lie side by side so as to occupy the interior space of a natural disc from which the nucleus pulposus has been removed. When any form of the prosthesis is used to replace a diseased or damaged spinal disc, proper spacing of the adjacent vertebrae is maintained and the prosthesis provides resistance to compressive forces imposed on the spine, as well as preserves the natural flexibility of the spine.