A finite element formulation for a saturated and partially saturated porous medium undergoing large elastic or inelastic deformations is presented. This model is derived from the general thermo-hydro-mechanical model for porous materials developed in a previous contribution of the authors to this lecture notes. The porous medium is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. The governing equations at macroscopic level are derived in a spatial setting. Solid grains and water are assumed to be incompressible at the microscopic level for simplicity. The consistent linearisation of the fully non linear coupled system of equations is derived. A spatial finite element formulation of the governing equations conclude this contribution of the authors.