This paper is intended to provide an accurate analytical solution to the I D differential equations modelling cyclic steady heat transfer processes in rapidly switched heat regenerators for any value of the flush ratio. The temperature solution for the fluid is initially given in an integral form along the path of a gas particle as a function of the matrix temperature for different space and time intervals. In particular, as a Lagrange system of reference is assumed, the above solution deals separately with gas particles of three possible types ('cold', 'hot' and 'internal') according to Organ's concept of independent flow regimes. Also, it accounts for the possible superposition of the so-called hot and cold zones of the regenerative matrix depending on the value of the flush ratio. Then, assuming a linear distribution for the matrix temperature, the fluid temperature may analytically be calculated. A closed-form expression for the regenerator effectiveness as a function of NTU and flush ratio is given. It provides a simple but accurate tool to estimate the regenerator effectiveness in rapid cyclic flow situations and the deriving results indicate that it is underestimated by the conventional regenerator theory. (c) 2007 Elsevier Ltd. All rights reserved.