In the present study, the flow of bulk materials is characterised as a non-Newtonian fluid and modelled using the lattice Boltzmann method. A power law and a Bingham model is implemented in the LBM, which is hydrodynamically coupled to the discrete element method (DEM) for structural interaction. The performance of both non-Newtonian models is assessed, both qualitatively and quantitatively, in benchmark problems. The validated, non-Newtonian LBM-DEM framework is then applied to the geometry of a cylindrical Couette rheometer to numerically determine the constitutive response of a sample of Leighton Buzzard sand. The numerical results, which employ the power law, are compared with experimental data, and a number of other synthetic soil samples are defined using the presented process of numerical rheometry. Finally, the numerical stress-strain rate response of the synthetic soil samples is interpreted within the context of a regularised Bingham model, and the similarities discussed. (c) 2011 Elsevier B.V. All rights reserved.