The goal of this work is to create a mathematical model for calculating the distribution of the local electric field near the field emitter in the form of a tip, taking into account the inhomogeneous surface structure on an atomic scale. In the course of the work, an edge shaped emission structure, approximated by a rectangular cylinder with an inscribed hemisphere on top, was investigated. The structure of a rectangular lattice is body-centered. As a result, a mathematical model of the crystallographic structure of the emitter surface was constructed, the distribution of the local electric field on the autoemitter surface was calculated by the finite difference method on a non-uniform grid using the Tapsim package.