In this document, computation of the corona discharge in a "cylinder-cylinder" electrode system is described. The Fokker-Planck equation is used to describe the kinetics of the electrons. The basic features of the physical process were observed in the solution. It shows that the stationary mode is possible only when the voltage is larger than a definite threshold value. One can discern two character areas between the electrodes. The internal area where the ionization is active and the current is carried both by electrons and ions has radius of 100-200 micrometers. The rest of the accommodation constitutes the drift area. The solution enables one to compare the illuminating zone and the zone of electrons multiplication. It revealed some features of rare gas discharge that preclude from directly applying the results of this work to discharge in air. Above all, it is a small value of negative charge density, which is caused by the electron conduction character in the external area. Nevertheless the solution of this model problem displays the wide possibilities of the method.