The role of the Cu atoms sputtered from the cathode material in a cylindrical hollow cathode discharge (HCD) and the corresponding Cu+ ions are studied with a self-consistent model based on the principle of Monte Carlo (MC) and fluid simulations. In order to obtain a more realistic view of the discharge processes, this model is coupled with other submodels, which describe the behavior of electrons, fast Ar atoms, Ar+ ions, and Ar metastable atoms, also based on the principles of MC and fluid simulations. Typical results are, among others, the thermalization profile of the Cu atoms, the fast Cu atom, the thermal Cu atom and Cu+ ion fluxes and densities, and the energy distribution of the Cu+ ions. It was found that the contribution of the Ar+ ions to the sputtering was the most significant, followed by the fast Ar atoms. At the cathode bottom, there was no net sputtered flux but a net amount of redeposition. Throughout the discharge volume, at all the conditions investigated, the largest concentration of Cu atoms was found in the lower half of the HCD, close to the bottom. Penning ionization was found the main ionization mechanism for the Cu atoms. The ionization degree of copper atoms was found to be in the same order as for the argon atoms (10−4).