The use of misfit strain to improve the electronic performance of semiconductor films is a common strategy in modern electronic and photonic device fabrication. However, pursuing a favorable higher strain could lead to mechanical instability, on which systematic and quantitative understandings are yet to be achieved. In this paper, we investigate the anisotropy effects on strain-induced thin-film surface roughening by phase field modeling coupled with elasticity. We find that compared with films grown along {111} and {100} surfaces, the instability of {110} film occurs at a much lower strain. Our simulations capture the evolution of interface morphology and stress distribution during the roughening process. Similar characterizations are performed for heteroepitaxial growth from a surface pit. Finally, from 3D simulations, we show that the surface roughening pattern on {110} film exhibits a clear in-plane orientation preference, consistent with experimental observations.