Computational models of dynamic ductile and brittle fracture are developed for wave propagation in one‐ and two‐dimensional geometries. The model features have been taken mainly from detailed observations of samples partially fractured during impacts, but the functional forms are consistent with theoretical results where applicable. Basic features of the models are the nucleation and growth (hence, the acronym NAG for the models) of voids or cracks, and the stress relaxation resulting from the growing damage. The results of the calculations include number and sizes of cracks, voids, or fragments as a function of position in the material. The NAG analysis presents the nucleation law, determined from experiment, and two growth laws: both growth and nucleation are functions of stress and stress duration. Procedures for treating cracks with a range of sizes and orientation are presented with the method for computing the stress relaxation that accompanies growth of damage. Brittle fracture is essentially anisotropic in actuality and in the model: cracks nucleate and grow as a function of stress normal to their plane, and the stress relaxation is a function of crack opening in the direction of the stress. Criteria are presented for the coalescence of cracks to form fragments and for complete fragmentation. The computational models have been applied to one‐ and two‐dimensional wave propagation problems. The NAG models have been shown to be applicable to several metals, a plastic, and a quartzite, to stress levels from just above threshold to ten times the threshold, and to load durations from 20 nsec to several microseconds. The damage has been computed for stress waves caused by impact, thermal radiation, and explosion.