Real-time Monte Carlo Molecular Dynamics (MC-MD) simulation techniques have been developed to model the nucleation, the initial stages of growth, and thin film growth, during InP Molecular Beam Epitaxy (MBE) on InP. The simulation mode includes tetrahedral lattice coordination, species-species interactions out to third-nearest neighbor, heterogeneous photolysis of precursors molecules on vacuum UV, adspecies migration on the lattice, nucleation on conventional and charge activated centers, and desorption dynamic effects. An InP homoepitaxy system, permits the simulator validation against MBE experimental results; although the model and the corresponding simulator are easily applied to a variety of other problems. The amount of InP epitaxy as a function of time is obtained over surface are of 50 X 50 atomic sites. The result of the simulations demonstrate that model treatment is accurate and encompasses several improvements over previous treatments. The agreement between experimental and simulated roughness serves to build confidence in the use of Mc-MD for MBE studies.