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The monolithic DPF made of cordierite ceramic has unsatisfactory on his fatigue or long-term strength. A new design of configuration of plugs combined with the hexagonal channels shows a transversally isotropic property, and can remove the anisotropy of monoliths with square channels. This anisotropy is assumed to be one of main reasons for the failure of monoliths with square channels regarding the experimental results. Considering the honeycomb structure as a homogeneous material based on the Boltzmann continuum can't give the correct behaviour of this structure in a FEM simulation. Another homogenization procedure using the Cosserat theory has been discussed. The FEM stress analyses with structural detail-models show that the maximal tensile stresses in the monolith with square channels exist in the diagonal (i.e. 45°-) direction, or on the edges of channels. This feature is identical with what the theory has predicted and the experimental results have shown.