AbstractA number of variational principles are established in this paper for the stress analysis of porous media with compressible constituents. A three‐dimensional finite element method is proposed based on the variational principle. The finite element method thus established is applied to the study of the temperature, deformation and flow field associated with the water‐flood technique in secondary recovery projects for oil exploration. In the study model, the layout of injection wells and production wells is considered to have a regular pattern where symmetry conditions exist. The injection fluid diffuses slowly into the formation through a vertical crack which is initially generated by an explosion. The problem is analysed by a plane strain formulation with the effects of heat conduction and convection inclu