We have developed a three-dimensional finite element method to simulate the morphological evolution of a strained surface via surface diffusion, with a view to understanding the self-assembly, shape transitions and stability of low-dimensional quantum structures. We model deposition of an elastic film on a large lattice mismatched substrate. The film surface evolves by surface diffusion, driven by a gradient of the surface chemical potential, which includes the elastic strain energy, elastic anisotropy, surface energy, surface energy anisotropy and the interaction between the film and the substrate. Our simulations reveal that surface energy anisotropy and elastic anisotropy have a strong effect on the morphological evolution and shape transitions of the self-assembled islands. Our simulation results show a good qualitative agreement with experimental results.