In this paper the mathematical modeling of the diode field emission system on the basis of field emitter as a semi-ellipsoid on a flat-surface substrate is considered. The anode is a semi-ellipsoidal surface. The internal area of the system is contained with two layers of different dielectrics. The boundaryvalue problem for the Laplace's equation in the prolate spheroidal coordinates is solved to found electrostatic field. The electrostatic potential distribution in analytical form is calculated with the method of separation of variables as the Legendre polynomials expansion.