In this paper, an efficient and robust algorithm has been developed for simulation of unsteady-state fixed-bed reactors with how reversal. This algorithm is based upon a rigorous dynamic heterogeneous model, which is solved by a hybrid procedure of discretization and integration. A modified nonequidistance finite-difference method, based on that of Eigenberger and Butt (1976, Chem. Engng Sci. 31, 681-691), is presented for discretizing the temperature profiles. The resulting ODEs defining solid-phase temperature ale solved by an explicit integrator proposed by Ashour and Hanna (1990, Comput. Chem. Engng 14, 267-272). SO2 oxidation over vanadium catalysts is presented as an example. The "wrong-way" behavior of the reactor has been discussed, with a critical feed temperature defined for its occurrence.