A differential-flow-induced instability, which generates travelling waves, may occur in the exothermic reaction A --> B + heat in a packed bed tubular cross-flow reactor. It is caused by the differential flow (not to be confused with cross flow) between heat acting as autocatalyst and the reacting matter, at elevated Lewis numbers. The uncoupling of heat and matter transport releases the inherent tendency of the autocatalyst to grow. A stability analysis of the governing equations is presented. Simulations of the travelling wave patterns show that multiple solutions coexist and are asymptotically stable.