Individuals genetically predisposed to cancer may be more sensitive to cancers induced by ionizing radiation than those who are not so predisposed. Should this be true, under conditions of radiation exposure, a population consisting of cancer-predisposed and non-predisposed individuals will be expected to respond with a higher total frequency of induced cancers than one in which all the individuals are assumed to have the same sensitivity to radiation-induced cancers. To study this problem quantitatively, we have developed a Mendelian autosomal one-locus, two-allele model; this model assumes that one of the alleles is mutant and the genotypes carrying the mutant allele(s) are cancer-predisposed and are also more sensitive to radiation-induced cancer. Formal analytical predictions as well as numerical illustrations of this model show that: (1) when such heterogeneity with respect to cancer predisposition and radiosensitivity is present in the population, irradiation results in a greater increase in the frequency of induced cancers than when it is absent; (2) this increase is detectable only when the proportion of cancers due to genetic predisposition is large and when the degree of predisposition is considerable; and (3) even when the effect is small, most of the radiation-induced cancers will occur in predisposed individuals. These conclusions are valid for models of cancer when predisposition and radiosensitivity may be either dominant or recessive. The published data on breast cancers in Japanese A-bomb survivors show that at 1 Sv, the radiation-related excess relative risk in women irradiated before age 20 is 13 compared to about 2 for those irradiated at later ages. We examined the application of our model to the above data using two assumptions, namely, that the proportion of cancers due to genetic susceptibility at the BRCA1 locus (1/200) and the frequency of the mutant allele (0.0033) estimated for Western populations are valid for Japanese women. With our model, these results can be explained only if there are very large differences in cancer susceptibility (>1000-fold) and radiosensitivity (> 100-fold) of the heterozygotes.