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A new approach for the fluid-dynamic simulation of the Diesel Particulate Filters (DPF) has been developed. A mathematical model has been formulated as a system of nonlinear partial differential equations describing the conservation of mass, momentum and energy for unsteady, compressible and reacting flows, in order to predict the hydrodynamic characteristics of the DPF and to study the soot deposition mechanism. In particular, the mass conservation equations have been solved for each chemical component considered, and the advection of information concerning the chemical composition of the gas has been figured out for each computational mesh. A sub-model for the prediction of the soot cake formation has been developed and predictions of soot deposition profiles have been calculated for different loading conditions. The results of the simulations, namely the calculated pressure drop, have been compared with the experimental data.