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A one-dimensional two-phase model of an adsorptive catalytic monolith reactor is used to analyze the Lean NOx Trap (LNT). The model simulates the features of NOx storage and reduction (NSR), a periodic process involving the sequential trapping on a storage component and conversion of NOx to nitrogen on a precious metal catalyst under lean conditions found in the exhaust of lean burn and diesel vehicles. A detailed storage kinetic model is used for the simulations. The NOx storage phase on Pt/BaO/Alumina catalyst has been studied in detail with particular attention to the effect of fluid velocity, storage time and storage component loading. The reductive phase is also analyzed. The simulated results are compared with our lab experimental data. The model predictions are in good agreement with the experimental observations and trends reported in the literature.