A biologically based probabilistic model of the carcinogenic process has been developed based on a two-stage theory of carcinogenesis. The model has been validated utilizing experimental urinary bladder carcinogenesis studies in the rat, with an emphasis on quantification of cell dynamics. Critical parameters tracked through this process include mitotic rates, cell loss and birth rates, and irreversible cellular transitions from normal to initiated to transformed states. Analyses demonstrate the sensitivity of tumor incidence to the timing and magnitude of changes to these cellular variables. Modeling has been applied to genotoxic compounds, such as N-[4-(5-nitro-2-furyl)-2-thiazolyl]formamide, and non-genotoxic compounds, such as sodium saccharin. For the latter compounds, complex administration regimens have been studied, including two-generation experiments, initiation-promotion experiments, and sodium saccharin administration following ulceration and regenerative hyperplasia. Modeling indicates that the effects of such compounds can be explained entirely on the basis of cytotoxicity and consequent hyperplasia. Quantitative modeling based on biological processes has the potential for direct application to carcinogenic risk assessment.