To obtain a longer power cycle length, the beginning-of-cycle excess reactivity of the reactor core must be increased. In the case of the Dodewaard reactor, this was done by raising the 235U enrichment of the fuel from 2.5 to 2.8%. To meet the shutdown margin criterion, the burnable poison, gadolinium, was added to 2 out of 36 fuel pins of each fresh fuel assembly. When a large number of these types of fuel assemblies are used to reload a reactor core, we must know the reactivity behavior of the hot operating core, as well as the variation in shutdown margin of the cold core as a function of burnup. By using a relatively simple analytical model, a reasonable prediction of these two phenomena could be made as shown by comparison with actual measurements and results of calculations with the FLARE computer code.