In this paper, we discuss two approaches to study the stress concentration and distribution around a cylindrical nanohole with undulated surface profile based on the first-order boundary perturbation technique and finite element method, respectively. To describe the effect of surface elasticity, the simplified formulation of Gurtin - Murdoch model neglecting the surface tension is used. Taking into account the plane strain conditions, the corresponding boundary value problem is formulated for a 2-D infinite domain with a nearly circular hole. The detailed numerical investigations are given to compare the first-order boundary perturbation and finite element solutions.