Equations for the deep bed filtration problems are obtained as a special case of a general model formulated earlier. The filtration coefficient λ is expressed as an explicit function of system parameters such as fluid flow rate, pore density, and pore size distribution. For a unimodal pore size distribution it is found that λ remains constant both in space and time. In general, however, λ is shown to decrease. Explicit solutions to the problem, including particle density profiles and permeability, are obtained for the two cases of large values of the coordination number Z (capillary tube model), and for a bimodal pore size distribution with a finite coordination number.