The main function of diesel particulate filter (DPF) is to remove the particulate matter (PM) from diesel engine emission. However, the accumulated PM restricts the exhaust flow through the DPF and increases the back pressure which may negatively impact fuel consumption. Therefore, the particulate filter needs to be regenerated by burning off the accumulated particulate, which is achieved either by passively use of a catalyst or by actively introducing high heat into the exhaust system.In the exhaust after treatment system considered in this paper, a diesel oxidation catalyst (DOC) is installed upstream of the DPF to facilitate the regeneration process. In order to combust the captured particulate in the DPF, a small amount of fuel can be injected into the exhaust, upstream of the DOC, when necessary. In an effort to develop a model-based control strategy which completes the regeneration while satisfies the constraints such as fuel consumption, temperature and regeneration period, a physics-based dynamic model of the DOC-DPF exhaust after treatment system is proposed. Parameters in the model including the heat transfer coefficient, reaction constants in the DOC and DPF, and the permeability of the filter and soot are identified based on the experimental measurements. The DOC-DPF model is then validated both at steady state and during transient against experimental data measured at various engine operating conditions, PM loads and fuel injection rates.