To develop vacuum electronics devices, it is necessary to take into account the influence of structural elements entering the system under investigation, in particular, composite layers with different dielectric permittivity values. In this paper a multipole electrostatic system is simulated, the inner region of which is filled with two different dielectrics. The multipole potential distribution defines 2N charged lines with a linear charge density with different signs on the adjacent elements. To solve the problem, the method of separation of variables is used. According to the given geometric parameters, the whole inner region was divided into two subregions. The potential distribution is represented as an expansion in eigenfunctions for each subregion. The fulfillment of the condition of the electric displacement vector normal component continuity at the interfaces of the regions made it possible to obtain a solution of the boundary value problem in an analytical form.