The bifurcation and instability conditions in geomechanics are closely related to the elasto-plastic behaviour. In this paper the potential of a multimechanism elasto-plastic model to predict various modes of failure is examined. First, a brief overview for the essential aspects of the constitutive model and the development of the elasto-plastic constitutive matrix for this model are presented. Then, numerical simulations of different drained and undrained paths in the axisymmetric and plane-strain conditions for the Hostun sand are illustrated. These examples confirm the capacity of the model to reproduce instability and strain localization phenomena. The obtained response is in agreement with experimental observations, theoretical developments and numerical analyses existing in the literature.