An approach is developed for understanding the cross-hatch morphology in lattice mismatched heteroepitaxial film growth. It is demonstrated that both strain relaxation associated with misfit dislocation formation and subsequent step elimination (e.g. by step-flow growth) are responsible for the appearance of nanoscopic surface height undulations (0.1-10 nm) on a mesoscopic (∼100 nm) lateral scale. The results of Monte Carlo simulations for dislocation- assisted strain relaxation and subsequent film growth predict the development of cross-hatch patterns with a characteristic surface undulation magnitude ∼50 Å in an approximately 70% strain relaxed In0.25Ga0.75As layers. The model is supported by atomic force microscopy (AFM) observations of cross-hatch morphology in the same composition samples grown well beyond the critical thickness for misfit dislocation generation.