[en] A simplified two-dimensional model which describes the inter-electrode region of a non-filtered vacuum arc with a cylindrical geometry is developed. The model includes elastic collisions and charge-exchange reactions between metallic particles and gas molecules, and also generation and recombination of gaseous ions by electron impact. The radial velocity component of the different particles is treated in the diffusive approximation. Solutions of the model corresponding to a copper-cathode continuous arc operating with a current of 100 A and oxygen filling gas with pressures in the range 0.5-50 Pa are presented