Catalytic combustion reactions and reacting systems that operate in the parameter sensitivity region of the kinetic regime are likely to experience sudden temperature changes, resulting in the development of thermal stresses in the catalyst support. The unified theory of Hasselman is used to study the onset and extent of crack propagation in catalyst support media. This theory is based on the principle that cracks propagate (terminate) when the total energy of the system increases (decreases) with additional crack growth. It is shown that the total energy of the medium (elastic and fracture energy) varies with time and position in the medium, and the extent of crack growth also varies from one point to the other. Within the limitation of the assumption that the crack density is low enough, the model provides valuable insight into the durability and mechanical strength of ceramic support media.