A mathematical model of a new reactor design has been proposed. In the new reactor the catalyst is deposited over the external surface of the tubes, where the coolant flows. The widespread industrial process of oxidation of o-xylene into phthalic anhydride was investigated. The results obtained show significant advantages of the new design in comparison with the conventional fixed bed reactor operating in the industry. They are: much higher productivity, easily controlled temperature regime, raised selectivity and decrease content of side products, as well as an opportunity for additional feed-in of the reagent along the reactor height. The technological regime of the oxidation process was optimized.