Molecular Dynamics (MD) simulations are performed on two-dimensional, triangular lattice models. The program used to perform these simulations was based on codes developed by Farid F. Abraham at the IBM-Almaden Research Center in San Jose, CA and by J.M. Haile, but also contained modifications to increase efficiency. These simulation models contain three constrained sides and a free surface, use a Lennard-Jones 6:12 interatomic potential, and initially exist with various amounts (∼ 5 to 10 %) of compressive strain. Our paper studies the formation of dislocations from atomic ledges during relaxation from a compressive state, as well as the subsequent motion of these dislocations. These simulations are particularly relevant to understanding morphological changes on the surface and nucleation of dislocations in heteroepitaxial thin films.