A boundary value problem on a circular nanometer hole in an elastic plane loaded at the boundary and infinity is solved. It is assumed that complementary surface stresses are acting at the boundary of the hole. Based on Goursat-Kolosov’s complex potentials and-Muskhelishvili’s technique, the solution of the problem is reduced to a hypersingular integral equation in an unknown surface stress. The solution of the problem shows that, due to an existence of the surface stresses, the stress concentration at the boundary depends on the elastic properties of a surface and bulk material, and also on the radius of the hole.