PURPOSE: Development of a model characterizing risk variation with RBE to investigate how the incidence risk for all solid cancers combined varies with higher neutron RBEs and different organ dose types. MATERIAL AND METHODS: The model is based on RERF data with separate neutron and gamma dose information. RESULTS: For both additive and multiplicative linear excess risks per unit organ averaged dose, a reduction of 50% in the risk coefficient per weighted dose arises when a neutron RBE of 110 is used instead of 10. Considering risk per unit liver dose, this reduction occurs for an RBE of 130 and for risks per unit colon dose for an RBE of 190. The change in the shape of the dose response curve when using higher neutron RBEs is evaluated. The curvature changed and became significantly negative for males at an RBE of 140 for colon dose, 100 for liver dose and 80 for organ averaged dose. For females this is the case at an RBE of 110, 80 and 60, respectively. CONCLUSIONS: Uncertainties in neutron RBE values should be considered when radiation risks and the shape of dose responses are deduced from cancer risk data from the atomic bomb survivors.