A model for description of the axial structure of a surface-wave-produced and -sustained plasma based on numerical calculation of a complete set of electrodynamic and kinetic equations is presented. The model includes a self-consistent solution to the electron Boltzmann equation, a set of particle balance equations for electrons, excited atoms, atomic and molecular ions, as well as Maxwell's equations with appropriate boundary conditions. A gas thermal balance equation is used to predict the neutral gas temperature self-consistently. Precise calculations of discharge characteristics of an argon plasma column sustained by an azimuthally symmetric surface wave at low and intermediate gas pressures have been performed. A comparison with available experimental data is done in order to test the validity of the model.