AbstractThe mathematical formulation and analysis of the Barenblatt–Biot model of elastic deformation and laminar flow in a heterogeneous porous medium is discussed. This describes consolidation processes in a fluid‐saturated double‐diffusion model of fractured rock. The model includes various degenerate cases, such as incompressible constituents or totally fissured components, and it is extended to include boundary conditions arising from partially exposed pores. The quasi‐static initial–boundary problem is shown to have a unique weak solution, and this solution is strong when the data are smoother. Copyright © 2002 John Wiley & Sons, Ltd.