Molecular dynamics simulations of the deposition of atoms on crystalline surfaces have been conducted using the embedded atom method. The following atom-substrate combinations have been employed: 0.1 - 40 eV Ag deposited on (111) and (100) Ag substrates; 0.1 eV Ag deposited on (100) Cu; and 0.1 eV Cu deposited on (100) Ag. The purpose of the calculations for Ag atoms deposited on Ag substrates was to investigate the effects of adatom arrival energy and substrate orientation on the interactions of low-energy atoms with crystal surfaces. The goal of tile Ag oil Cu and Cu on Ag calculations was to observe the mechanisms producing thepreviously-reported asymmetry in epitaxy for these systems. The Ag on Ag deposition simulations demonstrated that the effects of increased atom arrival energies in promoting layerby- layer film growth and producing diffuse substrate-filn interfaces (mixing) were basically the same on the (100) and (111) surfaces. At 0. 1 eV, representative of thennal evaporation, the degree of island formation on the (100) substrate was essentially tile same as previously reported for a (111) Ag substrate. At a given atom arrival energy between 10 and 40 eV, both the redistribution into full monolayers and the mixing by surface exchange interactions were seen to occur more readily on the close-packed (111) growth surface than on the more open (100) surface. The mixing was a stronger function of crystallographic orientation. Cu was observed to grow on (100) Ag as a (100)-oriented film, with the initial film layers transfonned essentially to the bcc structure by a Bain distortion, in agreement with various experimental results. The distortion of the film layers resulted in large-amplitude soft-mode (low-frequency) lattice vibrations. Ag was observed to grow on (100) Cu as a (111)-oriented film, as experimentally observed, with the <110>-type orientations of film and substrate parallel, as predicted by previous calculations of interfacial energy.