A boundary value problem on a circular nanometer hole in an elastic plane under remote loading is considered. It is assumed that complementary surface stresses are applied at the boundary of the hole. Based on Kolosov-Muskhelishvili's method, the solution of the problem is reduced to a singular integro-differential equation in an unknown surface stress. A solution to the obtained equation derived in an explicit form shows that, due to an action 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.