The incidence and growth rate of stomach cancer in the US population is modelled, for each sex, as a partially observed, discrete state stochastic process. Explicit evaluation of the transition rates between the states of the model is made possible by identifying them as specific functions of the time spent within each state. The functions used in the model were selected from the medical and epidemiological literature. With the model it was found possible to obtain fits to the age distribution of deaths due to stomach cancer for white males in 1975 and for selected age ranges for white females. These results suggested that the natural history of stomach cancer is different for females above and below age 65.