Based on the Gurtin—Murdoch surface/interface elasticity theory, the article investigates the effect of nonlinear terms in the boundary perturbation method on stress concentration near the curvilinear bimaterial interface taking into account plane strain conditions. The authors consider the 2D boundary value problem for the infinite two-component plane under uniaxial tension. The interface domain is assumed to be a negligibly thin layer with the elastic properties differing from those of the bulk materials. Using the boundary perturbation method, the authors determined a semi-analytical solution taking into account non-linear approximations. In order to verify this solution, the corresponding boundary value problem was solved using the finite element method where the interface layer is modelled by the truss elements. It was shown that the effect of the amplitude-to-wavelength ratio of surface undulation on the stress concentration is nonlinear. This should be taken into account even for small perturbations. It was also found that the convergence rate of the derived solution increases with an increase in the relative stiffness coefficient of the bimaterial system and, conversely, decreases with an increase of the amplitude-to-wavelength ratio.