The paper compares analytical and numerical solutions for two-dimensional solid mechanics problems of elastic bimaterial composites with a nanosized interface relief that arises on a boundary between two bulk layers and on an interface of a nearly circular inclusion. It is supposed that the uniform stress state takes place at infinity. Here, we use Gurtin - Murdoch model in which interphase domains are represented as negligibly thin layers ideally adhering to the bulk phases. Static boundary conditions at the interface are formulated according to the generalized Laplace - Young law. To solve corresponding boundary value we use first-order boundary perturbation method based on Goursat - Kolosov complex potentials. To examine the perturbation results, we use a finite element calculations.