In this paper, we discuss a theoretical approach to morphological instability analysis of the coherent interphase boundaries in strained heterostructures. Taking into account the fact that, under certain conditions, the atomic arrangement of solid–solid interfaces is thermodynamically unstable, the evolution equation describing the kinetics of the relief formation is obtained. The considered process is controlled by interface diffusion activated by the nonuniform stress field which occurs due to mismatch between materials and the initial interface perturbation. To define the stress distribution along the curved interface, we use constitutive equations of bulk and surface/interface elasticity modeling the interphase domain as a negligibly thin layer adhering to the bulk phases. This allows us to take into account the surface energy variation related to the interface relief evolution and analyze, in addition to other parameters, the effect of elastic constants that characterize the mechanical behavior of the interphase layer. With the use of the first-order approximation of the boundary perturbation method, the solution of the linearized evolution equation leads to an estimation of equilibrium surface shape.