Dynamic stress behavior during catalytic combustion of methane has been simulated under transient warm-up, cool-down, and cyclic conditions. The numerical model combines a two-dimensional solution to the transport equations, solution of an energy balance on the monolith wall, and the NIKE3D structural analysis code to predict thermal stresses. The model also includes a detailed heterogeneous kinetics model for a proprietary palladium oxide (PdO) catalyst, but the model ignores gas-phase reactions. Results illustrate that thermal stresses as high as 630 MPa can form during transient operating modes, which risks structural failure of the ceramic monolith. The maximum computed thermal stress concentrations occur near the inlet of the monolith. Peak transverse stresses (which act to form axial cracks) typically form near the inlet and centerline of the monolith structure, while peak axial stresses form near the edges of the flat plate that represents the monolith structure. Increasing the preheat temperature of the incoming fuel and air mixture lessens the peak thermal stress. To a first approximation, the magnitude of the peak transverse stress during any transient cycle considered with our model can be estimated from the maximum value of the gradient in the computed temperature profiles.