A regenerator operating under periodic conditions has been simulated on a digital computer by using a mathematical model. The governing equations are written in dimensionless form and the importance of several parameters is pointed out. Temperature histories within the refractory matrix are obtained as a function of time and two spatial dimensions, i.e., in the direction of fluid flow and perpendicular to it. Similarly, air and gas temperature histories are obtained as a function of time and distance during heating and cooling periods.