A theoretical model is proposed to define the failure criterion on an individual grain subjected to an arbitrary set of contact forces. The model is implemented in a two-dimensional computer simulation code based on the molecular dynamics method to study the crushing mechanisms of grains inside a granular material under oedometric compression. The simulation results are partially compared with experiments performed on granular packings composed of moulding plaster disks of uniform thickness under an oedometric compression, and a good agreement has been achieved.