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In this paper, we report the modeling of the selective catalytic reduction (SCR) of NOx using ammonia on a commercial vanadia-titania based catalyst. The model combines a steady-state two-dimensional channel model with a transient two- or three-dimensional monolith model of the whole catalytic monolith converter. The reaction mechanism includes the standard and fast SCR reactions and also the high-temperature oxidation of ammonia to model the decrease in conversion observed at higher temperatures. We used in-house experimental data spanning a wide range of inlet compositions and temperatures to validate the model. The model was found to be in excellent quantitative agreement with the experimental data.