Abstract: A two-dimensional model is presented that describes the behavior of argon metastable atoms, copper atoms, and copper ions in an argon direct. current glow discharge, in the standard cell of the VG9000 glow discharge mass spectrometer for analyzing flat samples. The model is combined with a previously developed model for the electrons, argon ions, and atoms in the same cell to obtain an overall picture of the glow discharge, The results of the present model comprise the number densities of the described plasma species, the relative contributions of different production and loss processes for the argon metastable atoms, the thermalization profile of the sputtered copper atoms, the relative importance of the different ionization mechanisms for the copper atoms, the ionization degree of copper, the copper ion-to-argon ion density ratio, and the relative roles of copper ions, argon ions, and atoms in the sputtering process. All these quantities are calculated for a range of voltages and pressures, Moreover, since the sticking coefficient of copper atoms on solid surfaces is not well-known in the literature, the influence of this parameter on the results is briefly discussed.