The plane problem for an elastic body containing a curvilinear defect under arbitrary remote loading is considered. The complementary surface stresses are acting at the boundary of the nanohole. It is assumed that a shape of the hole is weakly deviated from the circular one. Conditions at the boundary are formulated according to the generalized Laplace - Young equations. Using Gurtin - Murdoch surface elasticity model and Goursat - Kolosov complex potentials, the solution of the problem is sought by the boundary perturbation technique. For any-order approximation, singular integro-differential equation is derived. The algorithm of solving this equation is constructed. This solution and corresponding complex potentials for computing stresses are obtained for zero-order approximation and the effect of surface stresses is presented.