The effects of surface elasticity and surface tension on the stress field near nanosized surface asperities having at least one dimension in the range 1–100 nm is investigated. The general two-dimensional prob- lem for an isotropic stressed solid with an arbitrary roughened surface at the nanoscale is considered. The bulk material is idealized as an elastic semi-infinite continuum. In accordance with the Gurtin–Murdoch model, the surface is represented as a coherently bonded elastic membrane. The surface properties are characterized by the residual surface stress (surface tension) and the surface Lame constants, which dif- fer from those of the bulk. The boundary conditions at the curved surface are described by the general- ized Young–Laplace equation. Using a specific approach to the boundary perturbation technique, Goursat–Kolosov complex potentials, and Muskhelishvili representations, the boundary value problem is reduced to the solution of a hypersingular integral equation. Based on the first-order appro