Catalytic combustion of methane can generate thermal gradients that are large enough to shatter monoliths during several transient operating modes. This paper presents simulations From a 2-D transient numercial model of the transport and surface chemistry in a passage in a catalytic monolith, including convection and diffusion in the gas phase and heterogeneous reactions on the monolith walls. Rates of surface methane oxidation are based on reaction kinetics for a supported PdO catalyst assigned from differential reactor measurements. A thermal stress analysis package uses the predicted temperature profiles to calculate stress formation profiles in the monolith. The model neglects homogeneous reactions, but nevertheless describes the essential features of transient operating modes that generate the largest thermal stresses. Simulations are reported for inlet methane concentrations from 3 to 5 vol% in air and inlet temperatures from 300 to 500 degrees C. Results illustrate dynamic stress formation during combustor warm-up, cool-down and cycling of the inlet methane concentration, including cases with thermal stresses as high as 630 MPa, which exceed the fracture strength of typical monolith materials such as mullite and cordierite. The highest thermal stresses form perpendicular to the flow direction during warm-up transients, and would tend to crack the monolith walls along their axes.