Estimates are made of the risks to the Australian population as a function of age and gender for mortality or morbidity for all solid cancers after exposure to radiation. Excess relative risk (ERR) and excess absolute risk (EAR) models are used. The model coefficients are re-evaluated for radiation doses expressed as effective dose using data from the Japanese Life Span Study. Life-table methods are used throughout and the risk measures studied are: the risk of exposure related death, RERD and the risk of exposure related cancer, RERC. Australian life-table data and the age-specific cancer incidence and mortality rates of Australian males and females are taken from recent published tables. No dose and dose-rate effectiveness factor is applied. Sources of uncertainty used to calculate the confidence regions for the estimated risks include the statistical uncertainties of the model parameters and of the extrapolation of the risks beyond the period supported by the epidemiological data. Summary values of the risks are reported as averages of those calculated from the ERR and the EAR models. For males, the mortality risks per sievert range from 14% for 0-9 year age group, 7% at 30-39 years and 4% at 50-59 years. Corresponding values for females are 20%, 10% and 6%. Incidence risks are higher: for males the estimates are 32% for the 0-9 year group, 12% at 30-39 and 5% at 50-59. Corresponding values for females are 56%, 20% and 8%. The 90% confidence regions are about +/- 50% of these values. Estimates are given for the risks from CT whole-body scanning or virtual colonoscopy which could be used for cancer screening. If used at 3 year intervals and the effective dose per procedure is 10 mSv, then the RERD for males beginning screening at 40, 50 and 60 years is 0.4%, 0.3% and 0.1%, respectively and for females, 0.6%, 0.4% and 0.2%, respectively. RERD estimates for a 5 year interval between screens are about one-third smaller.