Composite materials are widely used in many branches of modern industry, because they have improved physical properties. However, in the process of manufacturing composites, roughnesses may appear on their interfaces, evolving during further operation. In this paper, we propose a theoretical method for analyzing the stability of the nanoscale topography of the heteroepitaxial material interphase taking into account its elastic properties based on the Gurtin - Murdoch model We use thermodynamic as well as surface and bulk elasticity equations, Goursat-Kolosov complex potentials, Muschelishvili representation and first-order approximation of boundary perturbation technique to solve the problem. An evolution equation is derived that gives the amplitude change of sinusoidal relief as a function of time, physical and geometric parameters of the problem.