A non-local description of nematic liquid crystals is presented. By considering a generic two body interaction, the total energy of a nematic sample is formally evaluated. It is given by a generalized non-local functional. The minimization of the total energy shows that the actual nematic tilt angle profile, characterizing the nematic director, is a solution of an integral equation that in the simplest case is of the Freedholm type. This new equation takes the place of the well known Euler-Lagrange equation used in the elastic theory of nematic liquid crystals. The existence of sub-surface deformations localized close to the limiting surfaces is studied by means of this integral equation. The analysis has been performed for cases of strong and weak anchoring, with and without external fields. The sources of the subsurface deformations are discussed in the framework of the usual Frank elastic theory.