The behaviour of a reverse flow reactor, designed for the purification of polluted air, has been studied. A heterogeneous, one-dimensional model has been solved by using an analytical approach and by using two different numerical algorithms. The calculations are mutually compared and with existing experimental data. No fitting of the model parameters to the data was employed and the agreement of all comparisons was good. Experimental data of a large-scale reverse flow reactor have recently been presented that allow for a final testing of the models. Again, the agreement between simulations and experiments was satisfactory. The computation time of the three solution methods is about the same, however, the analytical approach has advantages because it is, for example, more easy to handle in practice.