Abstract A phenomenological model that allows the correlation of pressure fields, filtration rate and cake thickness in the process that results from the axial flow of a suspension in a duct that is provided with a porous wall is presented. The model is based in the motion and the continuity equations for the phases and incorporates the following constitutive information: • Rheological properties of the suspension and of the fluid that makes up this suspension. • Rheological properties of the cake including the effects of the compressibility and the relation between the shear stress of mobilization and the normal stress associated to the Coulomb criterion in the stabilization of the thickness of the cake. • Properties of the filter medium. The experiments performed with an aqueous suspension of calcium carbonate (average particle diameter in the order of 0.5 μm) confirms the common knowledge that the properties of the cake depend on the mode of filtration, making it of capital importance to perform specific assays for each case that is studied.