This paper aims to illustrate how anisotropic elastic properties of the crystal substrate affect epitaxial surface evolution and pattern formation. Specifically, for Ge and SiGe films on silicon substrates of various surface orietations, it is shown that the elastic anisotropy plays an important role. However, it must be pointed out that the evolution dynamics of epitaxial surfaces can be much more complicated, due to the combination/competition of various anisotropic properties (e.g., surface energy, surface diffusivity, etc.). Furthermore, for some surface orietations. e.g., Si(111) and Si(113), discrete surface steps play critical roles in the nucleation and growth of epitaxial islands and other surface structures.