Wear resistance and oxidation resistance of polymer material or a polymer component for bioimplantation are improved by packaging a polymer object in a sealed gas impermeable package substantially free of oxygen, irradiating the package with penetrating radiation to an extent sufficient to effect a desired substantial level of cross-linking within the polymer, and warming the packaged object while maintaining an elevated hydrostatic pressure to cause gases released during irradiation to recombine, stabilizing the material against subsequent oxidative change. The pressure stabilization terminates active sites, substantially eliminating free radicals. When applied to finished parts, the process simultaneously hardens and sterilizes the parts without degrading mechanical properties or dimensions. When applied to bulk material or unfinished parts, the part may be subsequent machined or otherwise finished, and sterilized by any conventional means. The procedure achieves high levels of cross linking without increasing susceptibility to aging or chemical degradation.