In this paper, we present a three-dimensional (3D) numerical model that describes a high current vacuum arc in the subsonic regime between copper contacts under the influence of an axial magnetic field (AMF). The model is based on a MHD approach to the inter-electrode plasma and is realized with the commercial software Ansys Fluent. Only the plasma region is modelled. The behaviour of the copper electrodes is taken into account by specific boundary conditions. We describe the model, the boundary conditions and present the simulation results. Temperature profiles and electron and ion densities will be presented in a reference case. Based on this arc modelling, a parametric study on arc characteristics will be performed, including varying the AMF strength, the ablation rate and the current intensity.