A new simulation technique (three-dimensional dislocation dynamics) enabling the capture of a hardening effect in metals due to irradiation is reported. When bombarded with high-energy particles, metals accrue internal damage. In irradiated Pd, for example, damage takes the form of interstitial loops. Such loops are nano-sized and typically have a high number density. The stress field of a loop is given from dislocation theory. It is shown here the hardening is due to the elastic interaction of gliding dislocations with a high number or spatially dispersed interstitial loops. Results are found to correlate well with experiments.