A prosthesis for replacing or supplementing a nucleus pulposus of an intervertebral disk is an expandable container having flexible walls, the container being adapted to be inserted into a central cavity of an intervertebral disk through a narrow cannula, and the flexible walls are made from a biocompatible hydrogel. A preferred hydrogel is a cryogel formed from an aqueous solution of poly(vinyl alcohol) and poly(vinyl pyrrolidone). The prosthesis may be prepared by dip-coating a mandrel with an aqueous solution of a hydrogel-forming polymer or mixture of such polymers, gelling the coated solution by chilling, and subjecting the gelled coating to a series of repeated freeze-thaw treatments. In use, the prosthesis is inserted into a central cavity of an intervertebral disk and filled with biocompatible material, e.g., a biocompatible liquid, a biocompatible polymer, and a biocompatible hydrogel, particularly a thermogelling hydrogel.