Abstract: The invention provides a method for reducing or eliminating the odors commonly produced by the sterilization of polyolefin-based products by gamma radiation. In addition, the invention also provides a method for minimizing the amount of fabric strength loss associated with the irradiation process and a method for actually increasing the fabric strength of a polyethylene that has been irradiated. Both the reduction in odors and the minimization of strength or increase in polyolefin strength are achieved in methods comprising the use of an oxygen scavenger. The invention further includes the use of non-gamma stabilized polyolefins. The polyolefinic product may also include an odor mask that may be used to mask any residual odor.