Fluidised beds play an important role in physical and chemical engineering processing. Understanding the granular motion within these beds is essential for design, optimisation and control of such processes. Motion on the particle scale is difficult to measure experimentally, making computational simulations invaluable for determining the dynamics within such systems. Computational models which have had the greatest success at capturing the full range of dynamics are coupled discrete element model and Navier-Stokes solvers, based on a pressure-gradient-force formulation. However, most discrete element models assume spherical geometry for the particles. Particle shape in many important industrial processes, such as catalysis and pyrolysis, is often non-spherical. We present a reformulation of the pressure-gradient force model, based on a modified pressure correction method, coupled to a discrete element model with non-spherical grains. The drag relations for the coupling are modified to take into account the grain shape and cross-sectional area relative to the local gas flow. We show that grain shape has a significant effect on the dynamics of the fluidised bed, including increased pressure gradients within the bed and lower fluidisation velocities when compared to beds of spherical particles. A model is presented to explain these effects, showing that they are due to both decreased porosity within the bed as well as the relative particle cross-sectional area creating a greater net drag over the bed. Our findings will be of interest from an applied standpoint as well as showing fundamental effects of particle shape on coupled fluid and granular flow. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.