Results are presented of the computer simulation of medium-pressure RF discharge across a coaxial gap between long cylindrical electrodes. This type of discharge configuration is promising and is already being used in diffusively cooled lasers with a transverse RF-discharge pump. Two different discharge conditions were considered: first, when the external circuit contains a de-current blocking capacitor, and, second, when a de current passes in the discharge circuit. Since an asymmetric RF discharge is a source of de emf,then, in the first case, a constant potential difference appears on the electrodes, and, in the second case, a de current passes in the discharge. The simulation confirmed the applicability of the previously developed simple model of low-pressure asymmetric RF discharge to the case of medium pressures. The computer experiment made it possible to find out the exponent of a power relation between the ratio of near-electrode layer mean potentials and the ratio of electrode areas. This exponent has been experimentally determined for low-pressure asymmetric discharges. However, no such experiments have been conducted with medium-pressure discharges. Determination of this exponent makes it possible to apply the earlier developed simple analytical model to the medium-pressure asymmetric discharge, and to forecast the conditions that are unfavorable for laser operation.