An essential step in the improvement of design strategies for a wide range of industrial deep drawing applications is the development of methods which allow for the precise prediction of shape and processing parameters. Earlier work has demonstrated, in a clear but qualitative manner, the capabilities of the hierarchical multiscale (HMS) model, which predicts the anisotropic plastic properties of metallic materials based on a statistical analysis of microstructure-based anisotropy and a continuous description of the yield locus. The method is implemented into the ABAQUS finite-element software but, until recently, little attention had been paid to other factors which determine the accuracy of a finite element prediction in general, such as mesh size, friction coefficient and rigid/elastic modelling of the tools. Through the analysis of cup drawing, which is a well-established laboratory-scale test relevant to industrial applications, a quantitative comparison is provided between measured cup geometry and punch force and modelling results for commercial AA6016T4 aluminium sheets. The relatively weak earing behaviour of these materials serves to emphasise the small differences still found between model and experiment, which may be addressed by future refinement of the micromechanical component of the HMS. Average cup height and punch force, which is an important process parameter omitted in earlier studies, depend primarily on the friction coefficient and assumptions in the modelling of the tools. Considering the balance between accuracy and precision, it is concluded that the proposed methodology has matured sufficiently to be used as a design tool at industrial level.