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The stress–strain relations and the yield behavior of a model glass (a 80:20 binary Lennard-Jones mixture) [W. Kob and H. C. Andersen, Phys. Rev. E 52, 4134 (1995)] is studied by means of molecular dynamics simulations. In a previous paper [F. Varnik, L. Bocquet, J.-L. Barrat, and L. Berthier, Phys. Rev. Lett. 90, 095702 (2003)] it was shown that, at temperatures below the glass transition temperature, Tg, the model exhibits shear banding under imposed shear. It was also suggested that this behavior is closely related to the existence of a (static) yield stress (under applied stress, the system does not flow until the stress σ exceeds a threshold value σy). A thorough analysis of the static yield stress is presented via simulations under imposed stress. Furthermore, using steady shear simulations, the effect of physical aging, shear rate and temperature on the stress–strain relation is investigated. In particular, we find that the stress at the yield point (the “peak”-value of the stress–strain curve) exhibits a logarithmic dependence both on the imposed shear rate and on the “age” of the system in qualitative agreement with experiments on amorphous polymers [C. Ho Huu and T. Vu-Khanh, Theoretical and Applied Fracture Mechanics 40, 75 (2003); L. E. Govaert, H. G. H. van Melick, and H. E. H. Meijer, Polymer 42, 1271 (2001)] and on metallic glasses [W. L. Johnson, J. Lu, and M. D. Demetriou, Intermetallics 10, 1039 (2002)]. In addition to the very observation of the yield stress which is an important feature seen in experiments on complex systems like pastes, dense colloidal suspensions [F. Da Cruz, F. Chevoir, D. Bonn, and P. Coussot, Phys. Rev. E 66, 051305 (2002)] and foams [G. Debrégeas, H. Tabuteau, and J.-M. di Meglio, Phys. Rev. Lett. 87, 178305 (2001)], further links between our model and soft glassy materials are found. An example is the existence of hysteresis loops in the system response to a varying imposed stress. Finally, we measure the static yield stress for our model and study its dependence on temperature. We find that for temperatures far below the mode coupling critical temperature of the model (Tc = 0.435 in Lennard-Jones units), σy decreases slowly upon heating followed by a stronger decrease as Tc is approached. We discuss the reliability of results on the static yield stress and give a criterion for its validity in terms of the time scales relevant to the problem. © 2004 American Institute of Physics.