Solid-state deformation processing of crosslinked high molecular weight polymers such as UHMWPE, for example by extrusion below the melt transition, produces materials with a combination of high tensile strength and high oxidative stability. The materials are especially suitable for use as bearing components in artificial hip and other implants. Treated bulk materials are anisotropic, with enhanced strength oriented along the axial direction. The material is oxidatively stable even after four weeks of accelerated aging in a pressure vessel containing five atmospheres of oxygen (ASTM F2003). Because of its oxidative stability, the deformation processed material is a suitable candidate for air-permeable packaging and gas sterilization, which has thus far been reserved for remelted crosslinked UHMWPE.