The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube–packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non–spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.