A comprehensive computer program has been developed for the simulation of atomic-displacement cascades in a variety of crystalline solids, using the binary-collision approximation to contruct the projectile trajectories. The atomic scattering is governed by the Moliére potential. Impact-parameter-dependent inelastic losses are included using Firsov's theory. Thermal vibrations of the target atoms and crystal surfaces may be included. Permanent displacement of lattice atoms may be based on either an energy-threshold criterion or a Frenkel-pair-separation criterion. An extensive series of calculations has been made for cascades in the simple metals Cu, Fe, and Au, to test the effects on the results of many of the model parameters. When a displacement-threshold energy is used, the number of Frenkel pairs is found to be a linear function of that part of the primary recoil energy which remains as the kinetic energy of atoms. This result is independent of target temperature, of the presence or absence of inelastic energy losses, and of various details of the model. In contrast, when a separation criterion is used, the number of defects increases less rapidly than linearly. This effect is caused by increased recombination in the highly disturbed tracks of the energetic recoils. Agreement between theoretical and experimental estimates of the radiation damage produced by neutron irradiation of Cu is substantially improved in the latter model.