Thermal stresses constitute a major portion of the total stress which the ceramic wall flow filter experiences in service. The primary source of these stresses is the temperature gradients, both in radial and axial directions, which attain their maximum values during regeneration. The level of particulate loading, the flow rate, the filter size and the mounting design govern the severity of temperature gradients which, together with physical properties and aspect ratio of the filter, dictate the magnitude and distribution of thermal stresses. The filter, the mounting, and the regeneration conditions should be so designed as to minimize these stresses to insure reliable and fracture free performance of the filter throughout the lifetime of the vehicle.In this paper we present a thermal stress model, based on finite element method, which computes stresses in the axisymmetric filter subjected to linear or step temperature gradients in radial and axial directions. The model is useful for assessing the effects of aspect ratio and expansion anisotropy, both of which play a key role in filter design, and is illustrated by way of examples taken from simulated regeneration conditions.The importance of thermal fatigue in this application is also discussed.