Comprising metal, polymer, and ceramic matrices, entire classes of fiber composites are typical examples of heterogeneous materials. Fibers of varying diameters, from hundreds of microns to a few nanometers, are dispersed differently in various materials. The stress-strain state of near-surface and near-boundary layers in inhomogeneous systems significantly influences the strength and physicochemical properties of materials. The production of plastic deformation and fracture processes in these regions impacts the material’s overall mechanical behavior and is therefore highly relevant. The classical theory of elasticity may lead to imprecise assessments of acting stresses and deformations due to conventional evaluations of micro- and nanoscale heterogeneities. In this work, we present the problem of a nearly circular hole in a nanoplate in a case of plane stress, allowing for the surface elasticity and residual surface stress by the Gurtin – Murdoch model. The problem on a plane stress of a plate in the presence of the surface stresses differs essentially from the corresponding problem on a plane strain of a body, as the elastic parameters of the plate depend on the elastic parameters of the surface and plate thickness. The boundary conditions are derived according to the corresponding generalized Laplace – Young law. The boundary perturbation approach and the Goursat – Kolosov complex potentials allow reducing the problem’s solution to a sequence of singular integro-differential equations which can be solved using the power series algorithm. Based on the explicit forms of the analytical solution, we present numerical results for the stress field near the boundary of the nanopore given by the cosine function. The effect of plate thickness on the stress field at the surface of the pore and the role of surface tension at this surface is shown. Acknowledgements The research was supported by the Russian Science Foundation (project no.25-21-00202).