This paper presents the complex Green function for the plane-strain problem of an infinite, isotropic elastic plane containing a circular hole with surface effects and subjected to a force applied at a point outside of the hole. The analysis is based on the Gurtin and Murdoch [1975, “A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57, pp. 291–323; 1978, “Surface Stress in Solids,” Int. J. Solids Struct., 14, pp. 431–440] model, in which the surface of the hole possesses its own mechanical properties and surface tension. Systematic parametric studies are performed to investigate the effects of both surface elasticity and surface tension on the distribution of hoop stresses on the boundary of the hole and on a line that connects the point of the applied force and the center of the hole.