We propose a model to study, on an atomistic scale, the effects of elastic misfit strains on the growth and coarsening of domains in phase-separating alloys. The model considered is a two-dimensional square crystal lattice with periodic boundary conditions and with anA orB atom near each site. To model the elastic interaction, nearest and next-nearest neighbours are connected by springs with longitudinal and transverse stiffness. In addition, there is a chemical interaction between nearest neighbours, favouring like against unlike pairs. A mean field analysis predict phase separation into coherent phases, below a temperature which (for a typical set of elastic parameters) increases with the strength of the elastic forces. This critical temperature is less than that for separation into incoherent phases. The analysis also predicts how the anisotropy determines the shapes of domains at early times. A Monte Carlo procedure for implementing Kawasaki dynamics to represent diffusion in this model is described. © 1995 Acta Metallurgica Inc.