Bone and head sinus cancer incidence after ingestion of ²²⁶Ra and ²²⁸Ra by radium dial painters is analysed using a two-mutation clonal expansion model for radiation carcinogenesis, taking into account the retention and radiation patterns of these nuclides in the body. The best fit is obtained for compact bone retention and efficient diffusion of ²²²Rn to the bone cavities and radiation action on both mutation rates of the cancer model, as found in a similar analysis of bone sarcomas after ²²⁶Ra injection in beagles. The model parameters of the best fit are consistent with cellular radiobiological data and a previous analysis of lung cancer in uranium miners. Due to the low background incidence of bone and head sinus cancer, the resulting dose-effect relationships for these cancers are linear-quadratic with radium ingestion and alpha radiation dose. These results do not support a threshold dose concept, but the risks at low doses calculated by the model come out to about a factor 10 lower than using a linear extrapolation of the data to low doses, a procedure currently applied by ICRP and EPA. Furthermore, the model results indicate radiation risks at low doses to be related with background cancer incidence between relative and absolute radiation risk projections. The results, which are dependent on the model assumptions, might be more generally applicable for bone seekers and will therefore need further study to arrive at better radiation risk estimations.