A model of a weakly ionized, low-pressure positive column discharge is described. Of particular interest is the generation of atomic resonance radiation. The model computes species densities as a function of radial position using fluid continuity equations. Electron impact collision rates are found from the zero-dimensional Boltzmann equation. The appropriate electron impact cross sections, heavy particle collision rate coefficients, and radiative decay rates for xenon have been assembled from the literature, and are summarized. Model predictions compare favourably with measured axial electric field values in a xenon positive column discharge, while the model is found to overpredict the electron temperature at low xenon pressure.