This paper is devoted to a two-dimensional emission system with a blade-shaped field cathode mathematical modeling. The field cathode is located on a flat substrate covered with a dielectric layer. The anode is a plane parallel to the substrate. The effect of the field cathode on the electrostatic field distribution is simulated as the effect of the charged lines system. The cathode surface coincides with zero equipotential. To determine the potential distribution, the boundary problem for the Poisson equation in the Cartesian coordinate system is solved using the method of separation of variables. The solution is presented in an analytical form in the entire area of the system under study. All geometrical dimensions, the dielectric constant of the layer, the potential of the anode are the parameters of the problem.