In the present paper, we analyze the effects of nonlinear terms in the method of the small parameter for a plane strain problem of isotropic bimaterial solid with a nanosized interface relief. In this case constitutive relations are the equations of both surface and bulk elasticity. The conditions of mechanical equilibrium are described using the generalized Young-Laplace equation. At each step of the asymptotic approximation, the boundary value problem reduces to a hypersingular integral equation. The results of the effects of nonlinear terms are considered of a comparison of the maximum values of hoop stresses.