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An analytical model was developed to simulate both sulfur adsorption and desorption characteristics based on the laboratory determined parameters. Diesel Lean NOx Trap (LNT) was tested under laboratory conditions to examine desulfation (deSOx) characteristics. Effects of different Lean/Rich (L/R) cycling of Air-Fuel ratio during the deSOx mode were investigated. The gradient of adsorbed sulfur along the axial direction of the sample LNT was also examined. The gradient of sulfur deposit, together with different L/R cycling combinations for the deSOx mode was critical to develop the efficient sulfur removal strategies. The model considered energy and mass balances during sulfur adsorption and desorption modes to predict the catalyst temperature and the amount of sulfur adsorbed and removed. HC and CO oxidation reactions as well as the oxygen storage were considered to estimate heat generated by the exothermic reactions.