Abstract: A modified Crank-Nicolson method with non-equidistant space steps for solving the equations which describe fixed-bed catalytic reactors operated with periodic flow reversal has been presented. Its prime feature is the automatic positioning of grid points in the required region, thus reducing considerably the total number of grid points and hence the amount of computation time. This algorithm can be well suited to the dynamic reactor modelling for highly exothermic reactions in which steep concentration and temperature gradiants and moving profiles are commonly encountered. Numerical examples have been presented and theoretical predictions have been tested with experimental results of sulfur dioxide oxidation on vanadium catalyst.