Monte Carlo based microscopic techniques were used to study the stability and metastability of thin coherently strained layers of mismatched silicon-like semi-conductor material grown on the (111) silicon surface. The structural energy was calculated using three-body empirical potentials. For layers greater than roughly 20 A in thickness, the critical layer thickness associated with thermodynamic stability agrees quantitatively with continuum theory. For thinner layers, however, considerable variations from the continuum theory are found. For a strained layer six monolayers thick, the test system is found to be metastable against the nucleation of misfit dislocations to a lattice mismatch of approximately 11%, compared to the 4% equilibrium stability limit. Additionally, simulation of strained layer growth of two-dimensional Lennard-Jones crystal lattices has been performed using x.)lecular dynamics. In particular, we have studied the influences of lattice mismatch and substrate temperature on the growth, from the vapor phase, of overlayer material possessing a different bulk lattice constant than that of the substrate material. Simulation results predict that at substrate temperatures less than 50% of melting, epitaxial growth occurs for mismatch values less than 14% whereas above this value, defective growth is observed. At temperatures above 50% of the melt temperature, mass transport occurs across the layer interface and rapid diffusion is observed in the top-most atomic layers, resulting in liquid-like behavior in a thin layer over ordered strained layer crystal.