This thesis is dedicated to the study of structural and petroleum geology problems. To this purpose, a frictional elastoplastic law based on the Van Eekelen criterion is formulated, which avoids the classical drawbacks of the Drücker Prager criterion. Also, a 2D automatic adaptive re-meshing algorithm is developed for complex multidomains configurations, in order to overcome the limitation of the Lagrangian mesh. Details of the hydromechanical formulation implemented in the LAGAMINE FE code in a large strain context are presented. Application cases (reproduction of sandbox simulation, study of a hydrocarbon trap) concentrate on the study of the strain localisation and potential fracturation using different criteria. In the first case, re-meshing technique allowed to reproduce successfully analogue experiment of thrusting propagation. In the second case, a detailed study based on different initial conditions has brought new insight to the reactivated origin of some faults and has allowed to obtain information on the potential fracturing of the hydrocarbon reservoir unit. As an academic case, the study of anorthosite diapirism is carried out, which confirms the validity of the petrological model of diapirism. Eventually, the hydromechanical coupling effects between a layered porous medium and a fault are illustrated on a simple case.