Models for understanding the basic concepts of fine grinding and how they apply to the design of stirred media mills have not yet matured. While spherical media in tower mills has previously been studied, real grinding media shape in stirred mills can range from spherical (steel/ceramic balls) to highly non-spherical (sand or slag) resulting in very different media and grinding dynamics. Handling the contact mechanics of non-spherical particles is a challenge for numerical models, and very few studies dealing with non-spherical particle shape exist in the literature. Discrete Element Method (DEM) simulations of dry media flow in a pilot-scale tower mill are performed for four cases with different shaped grinding media, in order to understand how flow and energy utilisation within a stirred mill depend on media shape. Differences in media transport, stress distribution, energy dissipation, and liner wear were observed in the tower mill for the spherical and non-spherical cases. A significant departure from sphericity of the media leads to strong dilation of the bed, reduced bulk density, and a reduction in active volume and collisional power levels leading to a reduction in power draw for the mill. In addition, highly non-spherical media tend to pack tightly near the mill walls forming a near solid layer around the inside of the mill shell which results in poorer transport and mixing, as well as increased wear rates on the screw impeller. Grinding performance in stirred mills appears to deteriorate strongly when using highly non-spherical media. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.