Results of numerical simulations of discharge development in an air gap between electrodes covered with solid dielectric are reported. Temporal and spatial variations of gas discharge parameters, dynamics of surface charge accumulation on dielectric barriers and the corresponding behavior of electric field in the gas gap and in the dielectric layers are presented and discussed. Evaluation of calculated data allowed explaining phenomena observed experimentally in the similar electrode system with solid dielectric barriers, leading, in particular, to significant improvement of dielectric strength of the whole system.