The effect of hydrogen added to an argon glow discharge is investigated by use of a set of numerical models for the various species present in the plasma, i.e., argon gas atoms, electrons, fast argon atoms, argon metastable atoms, Ar+, ArH+, H+, H2+ and H3+ ions, H atoms and H2 molecules, sputtered Cu atoms and the corresponding Cu+ ions. These species are described by a combination of Monte Carlo and fluid models. The effect of hydrogen on various calculation results is investigated, such as the electrical characteristics, the density of the species and flux energy distribution functions, the relative contribution to production and loss processes for the various species, the sputtering rate and the ionization of copper. The hydrogen addition is varied from 0.1 to 10%, and the results are also compared to a pure argon discharge. The calculated electrical current and the density and flux of the electrons, Ar+ ions, argon metastable atoms, sputtered Cu atoms and Cu+ ions decrease considerably as a result of hydrogen addition. The densities of the hydrogen-related ions, i.e., ArH+, H+, H2+ and H3+, appear to achieve a maximum at a certain hydrogen concentration, whereas the densities of the H atoms and H2 molecules continue to increase with the addition of hydrogen. The calculated energy of the electrons, the various ions and the fast Ar0 atoms remains more or less unaffected by the hydrogen concentration. The relative contribution to the cathode sputtering by hydrogen-related ions, especially by ArH+, rises with hydrogen addition, but the overall sputtering flux is predicted to decrease. Finally, the ionization of the sputtered Cu atoms appears to decrease with hydrogen addition, mainly because of a drop in Penning ionization. The relative contribution of electron impact ionization seems to become relatively more important. This might explain observations in the literature in which a better correlation was reached in an argon–hydrogen discharge compared to a pure argon discharge, between measured relative sensitivity factors and values predicted by simple empirical equilibrium models.