This paper presents the results of mathematical modeling of a two-dimensional field emission system based on an arbitrary number of blade-shaped field emitters. The emitters are located on a flat substrate. The anode is a plane parallel to the substrate plane. Since the surface of each emitter can be considered a corresponding equipotential surface, the influence of the emitters is replaced by the influence of charged filaments to calculate the electrostatic potential distribution throughout the entire emission system. The Poisson’s equation solution with the boundary conditions of the first kind is found as a series of eigenfunctions, with the coefficients of the series explicitly defined. All geometric dimensions of the system and the potentials at the electrodes are the parameters of the problem.