Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major role in the development of microstructures. In order to elucidate the key effects of elastic stresses on microstructural evolution when more than two misfitting phases are present in the microstructure, we have developed a microelastic phase-field model in two dimensions to investigate microstructural evolution during phase separation in a ternary alloy system with coherent elastic misfit. Numerical solutions of a set of coupled Cahn-Hilliard equations for the composition fields govern the spatiotemporal evolution of the three-phase microstructure. The model includes elastic driving forces arising due to coherency strain interactions between the phases. We systematically vary the misfit strains (magnitude and sign) between the phases along with the bulk alloy composition to study their effects on the morphological development of the phases and the resulting phase separation kinetics. We also vary the ratio of interfacial energies between the phases to understand the interplay between elastic and interfacial energies on morphological evolution. The sign and degree of misfit affect strain partitioning between the phases during spinodal decomposition, thereby affecting their compositional history and morphology. Moreover, strain partitioning affects solute partitioning and alters the kinetics of coarsening of the phases. The phases associated with higher misfit strain appear coarser and exhibit wider size distribution compared to those having lower misfit. When the interfacial energies satisfy complete wetting condition, phase separation leads to development of stable core-shell morphology depending on the misfit between the core (wetted) and the shell (wetting) phases. © 2019