A mathematical model for a saturated and partially saturated non-isothermal porous medium is presented. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and gas, which may be either vapour alone or a mixture of dry air and vapour. The governing equations at macroscopic level are derived in a spatial setting using averaging theories. Finite kinematics is included in the model. The solid skeleton of the medium can undergo large elastic or inelastic deformations described in the framework of hyperelastoplasticity. The fluids are assumed to obey Darcy’s law.