[en] The development of a surface barrier discharge in air at atmospheric pressure under the action of a constant voltage of different polarity is simulated numerically. When the polarity of the high-voltage electrode is negative, the discharge develops as an ionization wave that moves along the dielectric surface. When the polarity is positive, the discharge develops as a streamer that first moves above the dielectric surface and then comes into contact with and continues to develop along it. In the case of a high-voltage electrode of positive polarity, the discharge zone above the dielectric surface is approximately five times thicker than that in the case of negative polarity. The characteristic aspects of numerical simulation of the streamer phase of a surface barrier discharge are discussed. The numerical results on the density of the charge stored at the dielectric surface and on the length of the discharge zone agree with the experimental data.