The aim of our work is to discuss how the surface displacements caused by an applied force can be used for the identification of defects placed in near-surface layers of the body. As an illustrative example of the possibility for such identification, the elastic problem for the half-space weakened by a circular hole is considered. First of all we present the complete and correct analytical solution of the plane elasticity problem for the concentrated force acting on the surface of a half-space with a hole. We describe the biharmonic stressfunction used for the derivation of stresses and strains in the half-space with a hole and the associated biharmonic function that allows to determine the displacement field. Both functions are given in the form of Fourier series with the compact coefficients. It is shown that the found analytical formulas of surface displacements give the way to find the circular hole diameter and position when the applied force and elastic modules of the material are known.