The use of catalytic monoliths in high temperature combustion applications means that heat exchange by radiation plays an important role. Initially, this paper derives the system of integral equations that is used to model radiative exchange in a catalytic monolith with square or circular channels. Since the system is often coupled with a complex system of differential and algebraic equations that models channel interaction and other processes in the catalytic combustor, a simple approximation to the integral equations is introduced to make the problem tractable. The approximation technique is compared, first with the numerical solution of the integral equation for a cylindrical single channel, and second with published data for a simple cavity. The results of these two exercises show that the integral equation system and its approximation yield similar results to other workers and hence are appropriate for the modelling situation.