Samples of pyrolytic graphite and nuclear graphite have been irradiated at 27 or 77 K with neutrons and electrons. The dynamic Young's modulus has been studied by an isochronal annealing method and the internal friction has been measured as a function of temperature. The modulus changes with irradiation dose and annealings have been interpreted using a model based on the pinning of basal dislocations by interstitial atoms. The anneals have revealed an additional effect which was attributed to bonds between interstitial defects and atoms in the adjacent graphite layers. The observed modulus annealing stages are consistent with results of several authors.