There has been a marked increase in the use of the discrete element method (DEM) in geomechanics in recent years. The way in which DEM simulations are set up can have a noticeable influence on the observed response. The conditions for quasi-static shearing in DEM simulations of granular materials were studied here within the critical-state framework of the soil behaviour. Thirty-two constant-p′ triaxial simulations were carried out from which the critical-state relationships were defined in the void ratio-mean effective stress and deviator fabric-mechanical coordination number planes. Clear trends were observed for the void ratio, the coordination number, and the deviatoric fabric at the critical state as the inertial number, I, was varied. The critical state relationships were aligned along distinct loci for each value of I. The critical state framework was used to show that there is an upper bound to the I values below which the simulation is quasi-static and that the observed behaviour is independent of the strain rate. The parameter I was shown to be a useful measure for assessing the quality of quasi-static DEM simulations.