To reduce particulate matter (PM) in diesel exhaust gas, a diesel particulate filter (DPF) has been developed. The thermal durability of existing platinum catalyst-supported DPFs is inadequate. We are focusing on a non-catalytic after-treatment of silicon carbide (SiC) fibers with highly thermal durability. In this study, we simulated the processes of soot deposition and oxidation. Results show that even in exhaust gas without soot, a complex flow pattern is observed. The porosity of the filter is not constant along the flow direction, and the pressure gradient varies. The friction factor is slightly larger than the predicted value by the empirical equation in uniform porous media flow. Since the soot deposition occurs inside the filter, the depth filtration by SiC fibers was confirmed. In addition, the effects of filter temperature and oxygen concentration are clearly revealed. That is, comparing the oxidation at 700 °C, the deposited soot amount at 1200 and 1400 °C is decreased by 60% and 92%, respectively. Raising the oxygen concentration from 10% to 20% increases the oxidation efficiency from 42% to 64%. Although more work is needed over a wide range of operating conditions, a combination of these two parameters is important to achieve the non-catalytic exhaust after-treatment.