We discuss the effect of elastic fields on the late stages of coarsening during a solid-solid phase transformation in a two-phase binary alloy. The treatment is valid for both isotropic and anisotropic media. We hypothesize that there exist regimes in which coarsening proceeds in a self-similar or scale invariant manner. We show that this hypothesis is self-consistent in the two limiting regimes in which elastic effects are either dominated by, or dominate, capillary effects; when these effects are comparable, no scaling solution exists. For nonvanishing misfits and for domain sizes smaller than a certain crossover length, we recover the classical Lifshitz-Slyozov law that the characteristic length scale l(t) of the system evolves in time as t 1 3. At intermediate values of l, there is a crossover regime in which no single power law is expected. For large values of l, elastically driven coarsening dominates, leading to a different growth law [l(t) ∼ t 1 2]. Theoretical work of others suggests that elastically driven coarsening occurs when the domains are elastically harder than the matrix. We estimate the value of l corresponding to the crossover region for the case of idotropic materials.