The mechanical response of cohesionless granular materials under monotonic loading is studied by performing molecular dynamic simulations. The diversity of shapes of soil grains is modelled by using randomly generated convex polygons as granular particles. Results of the biaxial test obtained for dense and loose media show that samples achieve the same void ratio at large strains independent of their initial density state. This limit state resembles the so-called critical state of soil mechanics, except for some stress fluctuations, which remain for large deformations. These fluctuations are studied at the micro-mechanical level, by following the evolution of the co-ordination number, force chains and the fraction of the sliding contacts of the sample. Copyright © 2007 John Wiley & Sons, Ltd.