A model of filtration in a multispecies porous medium accompanied by a strong interaction between the flow and the porous matrix is presented. The species removed by the flow are both fine particles and other substances which diffuse in the liquid. The accumulation of the migrating particles in proximity of the outflow surface gives rise to the formation of a compact layer with high hydraulic resistance. The corresponding mathematical model consists in a set of partial differential equations of hyperbolic and parabolic type. to be solved in a free domain: the free boundary is the surface separating the compact layer from the rest of the medium. Under specific assumptions, which are expressive from the physical point of view, a result of existence (globally in time) and uniqueness of the solution can be proved, by means of fixed point techniques. Finally, some qualitative aspects of the solution are examined.