A displacement based 3D finite element model is developed to simulate thermal stress induced by high temperature and temperature gradient during diesel particulate filter (DPF) regeneration. The temperature field predicted by 3D regeneration model from previous work is used as input. This finite element model agrees well with commercial software. It is a self-contained package capable of implementing meshing body, assembling global stiffness matrix and solving final equilibrium equations. Numerical simulation indicates that it is peak temperature rather than temperature gradient that leads to higher compressive thermal stress during regeneration. The maximum stress always appears at the channel corner located at the end of DPF. Parametric studies are performed to investigate the effects of DPF design on pressure drop, regeneration temperature, and thermal stress. This model provides insights into the complicated DPF working mechanism, and it can be used as design tools to reduce filter pressure drop while enhance its short term and long term durability.