High-entropy alloys (HEAs) are characterized not only by high values of entropy but also by high atomic-level stresses originating from mixing of elements with different atomic sizes. Particle irradiation on solids produces atomic displacements and thermal spikes. The high atomic-level stresses in HEAs facilitate amorphization upon particle irradiation, followed by local melting and re-crystallization due to thermal spikes. We speculate that this process will leave much less defects in HEAs than in conventional alloys. For this reason, they may be excellent candidates as new nuclear materials. We discuss initial results of computer simulation on model binary alloys and an electron microscopy study on Zr-Hf-Nb alloys, which demonstrate extremely high irradiation resistance of these alloys against electron damage to support this speculation.