A novel, packed-bed, reverse flow reactor is provided for the endothermic dehydrogenation of ethylbenzene to styrene. The catalyst bed is flanked by inert end sections to prevent the occurrence of the reverse reaction. Ethylbenzene vapor is added at one end of the reactor while superheated steam is added concurrently at a downstream location. The flow direction is periodically reversed by alternating the ethylbenzene introduction between the reactor ends and the steam introduction between axially symmetric locations away from the reactor ends. Employing a steam to ethylbenzene feed ratio of 8:1 to 10.2:1 (as compared to 12:1 to 17:1 employed during conventional adiabatic operation), it is shown that the proposed reverse flow operation produces reactor temperatures that are hundreds of degrees higher than the mixing cup temperature of the feed streams. While catalyst temperatures are at a maximum when the steam is introduced midway between the reactor ends, splitting the steam addition among multiple axially symmetric locations produces lower and more uniform temperatures that are better suited to providing optimum ethylbenzene conversion and styrene selectivity while maintaining efficient utilization of the added energy.