The study deals with a non-stationary process of mass and heat transfer accompanied by a chemical reaction occurring in a catalytic reactor. The process has been described by a one-dimensional continuous two-phase model of the reactor. Based on the assumptions of the ＇＇ideal thermal front＇＇ in the reactor, approximate solutions are obtained for the equations that describe the process. Relations are thus derived which define the principal properties of the thermal front, namely, its propagation velocity in the bed and the maximum temperature of the front. The above relations express these properties in terms of dimensionless numbers that characterise the chemical reaction taking place in the reactor and the operating parameters of the vessel. The formulae derived may be useful in the design of reactors with the periodic reversal of the feed mixture. They enable the effect to be analysed of the various operating parameters upon the propagation velocity of the thermal front and its maximum temperature, without resorting to tedious and time-consuming trial and error methods that require repeated integration of the model equations.