Abstract. The propagation of the long cathode-directed streamer in air is simulated in the approximation of a fixed radius of the streamer channel. The results of the simulation turn out to be sensitive to the channel radius and to a model of charged particle kinetics. A model including ionization expansion of the streamer channel and yielding results which depend only slightly on the initial channel radius is developed. For the streamer's propagation in a non-uniform field, our calculation agrees well with the available experimental values of the total anode current, the streamer length and the average electric field in the streamer channel. Simulation of the streamer's evolution in a uniform electric field shows a steady propagation if the field exceeds 8-8.5 kV cm −1 .