We investigate the interdependent processes of strain and diffusion in the formation of holes and atolls obtained by rapid annealing of Ge/Si(111) islands at T ≈ 970 °C. We show that the shape evolution from islands to atolls and holes is closely captured by an analytical model including strain-driven diffusion. In the model, strain profiles obtained by finite element solutions of continuum elasticity equations are introduced in the diffusion equation as the source of a diffusion flux driven by the strain gradient. When the shape of the elastic field in Ge/Si(111) islands is coupled to diffusion, the morphology of the SiGe nanostructures observed after annealing is reproduced.