When a metallic alloy is quenched into a miscibility gap, a mixture of two phases develops, whose domain structure then coarsens because of the interfacial energy between the two phases. This spatial arrangement of the domains and the rate at which they evolve may be strongly influenced by elastic interactions. In a recent paper, the authors described a method for simulating the effect of anisotropic elastic interactions in a two-dimensional Ising model of a cubic alloy, using Kawasaki dynamics with the elastic interactions represented by a long-range two-body interaction potential. Here we present the results of such simulations at various temperatures, alloy compositions and misfits (by "misfit" we mean the difference in size between the two kinds of atom), exhibiting snapshots both of the microscopic configurations (corresponding to experimental measurements using transmission electron microscopy) and of their squared Fourier transforms (corresponding to measurements using small-angle X-ray or neutron scattering). The anisotropy of the two-phase structure increased with time, misfit and composition but decreased with increasing temperature. The rate of coarsening of the domains was found, surprisingly, to be roughly independent of the misfit at a given value of temperature relative to the critical phase transformation temperature. Copyright © 1996 Acta Metallurgica Inc.