We present a calculation of the displacement rates and freely migrating defect production caused by neutron and gamma irradiation and their roles on causing irradiation hardening in a BWR core shroud. We find that the neutron displacement rate is much higher than the gamma displacement rate, but that the freely-migrating defects produced by gamma irradiation are significant compared to those produced by neutrons. We evaluate the influence of gamma and neutron irradiation on hardening using a point defect clustering model. We find that the influence of gamma irradiation on radiation hardening in the core shroud is small compared to that for neutron irradiation.