A method of producing an improved polyethylene, especially an ultra-high molecular weight polyethylene utilizes a sequential irradiation and annealing process to form a highly cross-linked polyethylene material. The use of sequential irradiation followed by sequential annealing after each irradiation allows each dose of irradiation in the series of doses to be relatively low while achieving a total dose which is sufficiently high to cross-link the material. The process may either be applied to a preformed material such as a rod or bar or sheet made from polyethylene resin or may be applied to a finished polyethylene part. If applied to a finished polyethylene part, the irradiation and annealing must be accomplished with the polyethylene material not in contact with oxygen at a concentration greater than 1% oxygen volume by volume. When applied to a preform, such as a rod, the annealing of the bulk polymer part of the rod from which the finished part is made must take place on the rod before the implant is machined therefrom and exposed to oxygen.