The application of a newly developed computational tool, DETCHEMMONOLITH, for the transient two- and three-dimensional simulation of catalytic combustion monoliths is presented. The simulation is based on the coupling of a transient 2D/3D heat balance of the solid monolith structure with steady-state calculations of the reactive flow in a representative number of channels. The two-dimensional single-channel model uses a boundary-layer approximation including detailed models for heterogeneous and homogeneous reactions as well as transport phenomena. As an example, the computational tool is applied to study the hydrogen-assisted catalytic combustion of methane in a platinum-coated honeycomb monolith.