Abstract: An algebraic multigrid method is developed to solve fully coupled multiphase problem involving heat and mass transfer in deforming porous media. The mathematical model consists of balance equations of mass, linear momentum and energy and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressure, gas pressure and displacement. The gas phase is considered to bean ideal gas composed of dry air and vapour, which are regarded as two miscible species. The model makes further use of a modified effective stress concept together with the capillary pressure relatio nship. Phase change is taken into account as well as heat transfer though conduction and convection and latent heat transfer (evaporation-condensation). Numerical examples are given to demonstrate the computing efficiency of this method.