The dynamics of epitaxial growth of metal films on FCC(001) metal substrates are investigated in this dissertation. This work focuses on understanding the details of two elementary steps of film growth. First, single metal atom deposition on FCC(001) metal substrates of the same atom type are investigated. The molecular dynamics (MD) method is used to determine the extent of ballistic or transient mobility of the adsorbing atom in the Ni, Cu, Rh, Pd, Ag, Pt, and Au systems. The general lack of ballistic adatom motion in these systems is explained in terms of an efficient transfer of energy between the adsorbing atom and the substrate;The diffusion of a single metallic adsorbate on the surface of a FCC(001) metal is also examined. The MD method is used to simulate the long-time motion of an adsorbed atom in the Ag on Ag(001) and Rh on Rh(001) systems. The MD results confirm that diffusion in these systems occurs via an independent activated hopping mechanism making it possible to apply simple kinetic models of diffusion. Transition state theory (TST) is then used to extract diffusion parameters from a realistic potential energy surface for all adsorbate/substrate combinations of Ni, Cu, Rh, Pd, Ag, Pt, and Au. The TST results indicate that the diffusion rate is primarily a property of the adsorbate;The molecular dynamics calculations in this work are all performed with the computer program SCT89. SCT89 is a general code for the simulation of processes on surfaces. It offers a myriad of options including scattering from clean and adsorbate covered surfaces, overlayer dynamics, and mapping of adiabatic potential energy contours. Incorporation of the MD/MC-CEM potential energy function provides consistent treatment of up to four chemically distinct species. It also features a user-friendly interface which is capable of creating its own input files. The writing of this code represents a major accomplishment, therefore a description of its construction and features is included in this dissertation.