Diesel Particulate Filters (DPFs) are probably the most effective means for trapping the exhaust emitted particulate from diesel engines. Foam type filters become a promising alternative to the common wall flow filters, since they are effective in filtering small size particles and provide a larger specific surface area for catalytic coatings. A mathematical model taking into account the significant phenomena during the dynamic filtration of foam filters is developed. The model predicts the filtration efficiency and the induced backpressure as function of the geometric filter properties and operating conditions. A novel approach is employed which considers both "deep-bed" and "cake" filtration characteristics in the filter. Due to the particular structure properties of the foam filters it is necessary to define a characteristic parameter, which differentiates among different filter types. This parameter, which has a physical meaning, is easily derived by simple experimental measurements. The model is employed to identify and understand the critical parameters of the phenomenon. Indicative parametric runs are presented, which illustrate the applicability of the model in system optimization procedures.