To improve air pollution, we must reduce soot particulates in vehicle exhaust gas, which are inevitably harmful to the environment as well as to human health. Many countries are setting new regulations of nanoscale particle emission. Then, a ceramic porous filter such as diesel particulate filters (DPFs) has been developed. However, as more particles are trapped within their wall pores, the pressure difference (drop) across the filter increases. Resultantly, this situation could worsen the fuel efficiency, simultaneously with less torque. Usually, the filter regeneration process for particle oxidation inside the filter should be periodically needed. Thus, a filter with lower pressure drop would be preferable. In the current stage, the responses of the pressure drop during both particle filtration and oxidation are not fully understood. This is because these are the small-scale processes, and we cannot observe the internal physical phenomenon experimentally. In this paper, focusing on the exhaust flow with soot particles, the filtration was numerically simulated by a so-called lattice Boltzmann method (LBM). Here, the time-variation of the filter-back pressure was evaluated, which is important for the transport phenomena in the porous filter. For comparison, the pressure drop during the filter regeneration was also simulated to show the different pressure response affected by the soot oxidation zone.