The thyroid cancer data of children in the northern regions of the Ukraine after the reactor accident at Chernobyl were combined with thyroid dose measurements in the same regions and analysed using a two-mutation carcinogenesis model. The best fit was obtained for radiation acting as an initiating agent, i.e. on the first mutation of the model. The observed relatively high increase of thyroid cancer incidence after 1990 in children exposed to radiation released after the reactor accident could be ascribed to the high thyroid doses and the relatively low background thyroid cancer incidence in children. The maximum annual incidence is predicted to occur fairly soon after the reactor accident, i.e. about 10 years. For adults, the predicted relative increase of annual thyroid cancers is much lower than for children younger than 20 years. The modelling results are used to derive risk estimates for radiation-induced thyroid cancer. These risk estimates are dependent on age at exposure, follow-up time and the background thyroid cancer incidence. The calculated excess absolute risk for a population of all ages is about one-third of that currently used by ICRP, but for children the calculated absolute risks are about a factor of 3 higher than derived in other epidemiological studies. The model results indicate that the excess absolute radiation risk per unit dose for children is about the same as or a little lower than that for adults.