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 oe dometric compression. The simulation results are partially compared with experiments performed on granular packings composed of moulding plaster disks of uniform thickness under an oe dometric compression, and a good agreement has been achieved.