Irradiation effects in polyethylene and cellulose were examined using molecular dynamics simulations. The governing reactions in both materials were chain scissioning and generation of small hydrocarbon and peroxy radicals. Recombination of chain fragments and cross-linking between polymer chains were found to occur less frequently. Crystalline cellulose was found to be more resistant to radiation damage than crystalline polyethylene. Statistics on radical formation are presented and the dynamics of the formation of radiation damage discussed.