Abstract A two-dimensional model of an elastic body at nanoscale is considered as a half-plane under the action of a periodic load at the boundary. An additional surface stress, and constitutive equations of the Gurtin-Murdoch surface linear elasticity are assumed. Using Goursat-Kolosov complex potentials and Muskhelisvili technique, the solution of the boundary value problem in the case of an arbitrary load is reduced to a hypersingular integral equation in an unknown surface stress. For the case of a periodic load, the solution of this equation is found in the form of Fourier series. The influence of the surface stress on the stresses at the boundary of the half-plane under the tangential and normal periodic loading is analyzed. In particular, it is found out the size effect which becomes apparent in the dependence of the stresses on a length of the load period of the order 10 nm. Moreover, the tangential stresses appear under the action of the normal loads
