Intuitively, filtration occurs in a porous medium when the transported particles are actually sieved by the solid porous fabric, thereby decreasing the porosity and possibly clogging the medium (colmatage). This clearly can, and will, occur when the average size of the pores is smaller than that of the particles in solution, as in the case of large molecules, bacteria or colloids, migrating through clayey soils. But, in hydrogeology and in chemical engineering, filtration also refers to the mechanisms of retention when smaller particles form sediment in domains with large porosity. For example, deep bed filtration is the practice of removing suspended particles from a fluid stream by passing the suspension through beds composed of granular material. As the suspension flows through the granular bed, some of the particulants come in contact with the filter grains and become deposited onto the grains and onto particles already accreted. These changes affect the flow of the suspension through the porous medium and the subsequent deposition. In this chapter we introduce some models of filtration in the latter case. The difference between the adsorption models discussed in Chapters 1 through 3 and the filtration models discussed below is that filtered particles have volume, and when these particles are accreted by the soil matrix, the porosity of the porous domain decreases. Thus, the porosity is not constant. In the adsorption problems studied earlier the porosity remained constant because the volume of the accreted particles, e.g., ions, was considered negligible.