A method of calculating the reactivity and burn-up hisotry of a Mk.III GCR system containing burnable poisons has been described. The method allows for poison-fuel interaction. Using the method it has been shown that burn-up of the poison under a constant incident flux can give errors of the order of 1-2 niles. A calculation using the method described will take about 50% longer than a straightforward fuel burn-up calculation in the same number of groups. The multi-cell approach has a potential for handling greater geometrical complexity. It is intended to compare the method against experiment as soon as suitable experimental results become available.