Employing the original Gurtin-Murdoch model of surface elasticity, we
investigate the stress field near the curved surface of isotropic elastic solid jointly
induced by surface stresses and external tensile loading. Due to the plane strain conditions,
the two-dimensional boundary value problem for half-plane with a curved
boundary is formulated in terms of the complex variables. Based on the Goursat-
Kolosov complex potentials and boundary perturbation method whereby the unknown functions are sought in the form of a power series in the small parameter represented by an amplitude-to-wavelength ratio of the surface undulation, the formulated boundary value problem is reduced to the recurrent sequence of the integral equations for any-order approximation. Considering the cosine-shaped surface, the first-order approximation of the stress tensor components is derived in the closedform. The effect of the surface elasticity and surface tension on the stress field at the surface is numerically investigated.