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The multiplicative model for estimating incremental cancer risks linked with chemical-specific exposure is developed. The distinguishing feature of the model is that the additional cancer rate in the result of exposure to carcinogenic chemicals changes with age as a value proportional to the background cancer at this age. The proposed methodology enables assessing excess relative risk taking into account age and sex structure of background cancer rate in the exposed population, as well as the existence of a latent time between an exposure and an onset of disease. The model also enables estimating the environment pollution-related health damage, defined as the expected number of lost years of forthcoming life in the result of exposure. The model could be of value for the regulatory community and scientists in projecting a chemically-induced increase in cancer rate in one population to increases in cancer rates in other populations.