It is known that aromatic hydrocarbons are more stable to ionizing radiation than are saturated hydrocarbons. It is shown here that polyethylene can be more stable to radiation either by mixing aromatic compounds with the polyethylene or by grafting styrene onto the polyethylene. In either case, the polymer has greater radiation resistance than predicted from the law of averages. Aromatic compounds which have the greatest resonance energy protect the polymer to the greatest extent. In mixtures, polystyrene gives the least protection, and naphthalene, anthracene, and phenanthrene give the greatest protection. Polyethylene grafted with styrene has better radiation resistance than does a polyethylene-polystyrene mixture. The G(H2) was calculated for each sample, and curves are presented illustrating the effect.