A new method to model the abrasion of granular particles using the discrete element method is demonstrated in this paper. This new, simple method is based on a classical theory of abrasive wear, relating the volume of solid lost to the frictional work at particle contacts. The modelling technique is demonstrated in simulations of railway ballast using realistically-shaped particles, which are compared to experimental data. The new abrasion model correctly introduces stress-dependent behaviour at small strains into the simulations, which is essential for any realistic discrete element model. (C) 2020 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.