The Plasimo modelling platform, extended with a cathode wall sputtering module is used to study the discharge processes and to optimise the design parameters of a sputtering hollow cathode discharge (HCD). We present Plasimo simulations of a HCD used for laser applications. A time dependent sub-model is used to describe the behaviour of the plasma species. The sputtering yield at the metallic boundaries is calculated using an empirical formula. Copper is chosen as the cathode material and the discharge operates in helium with a small admixture of argon for more efficient sputtering. The optimal conditions for lasing of the infra-red (IR) copper ion line (780.8 nm) that have been determined experimentally are used as input conditions for the simulation model. Calculations are made for various gas mixtures. The observed quantities are compared with the experimental data obtained for the same discharge geometry and operating conditions. The agreement between the measured data and the results from modelling indicates that the main reactions in the model are correctly described. Therefore, it is believed that this model can be used as a design tool in optimizing discharge studies for various applications based on the sputtering of the cathode material.