A model of the negative glow of a low‐pressure Hg‐Ar discharge is described. The model contains a number of important physical processes (in particular noble‐gas excitation and multiple‐step ionization) that have not been included in earlier models. The model has also been coupled to a simple description of the Faraday dark space to enable predictions to be made of the axial density and potential profiles across the whole negative‐glow Faraday dark‐space positive‐column region. Results of a number of numerical computations are presented and in general these have been found to be in agreement with experimental observations. The effect of varying the various input parameters to the model on its predictions has also been studied and the results of this will also be presented.