A one-dimensional two-phase model of an adsorptive catalytic monolith reactor is developed and analyzed. The model simulates the generic features of NOx storage and reduction (NSR), a periodic process involving the sequential trapping on a storage component and conversion of NOx to nitrogen under lean conditions found in the exhaust of lean burn and diesel vehicles. The reactor model includes a phenomenological microkinetic model of NSR on a bifunctional storage catalyst. We examine the effects of several design and operating parameters on the reactant conversion, including cycle timing, feed flowrate, composition, and temperature. The simulations reveal complex spatio-temporal phenomena in the form of traveling concentration and temperature waves. The extent of site blocking by oxygen of NOx adsorption is an important determinant of cyclic enhancement of the NOx conversion. The model predictions are in qualitative agreement with experimental observations reported in the literature. For example, the NOx conversion exhibits a maximum at an intermediate cycle time and increases with decreasing rich pulse duty.