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.