Abstract: Computer simulations have been performed to describe the effect of small admixtures of hydrogen to an argon glow discharge in the Grimm-type configuration. The two-dimensional density profiles of the various plasma species (i.e., electrons, Ar+, ArH+, H+, H2+ and H3+ ions, H atoms and H2 molecules, Ar metastable atoms and sputtered Cu atoms) are presented for 1% H2 added to the argon glow discharge, and the effect of different H2 additions (varying between 0.1 and 10%) on the species densities, the hydrogen dissociation degree, and the sputtering process, are investigated. Finally, the relative contributions of various production and loss processes for the different plasma species are calculated.