A stochastic two-stage cancer model is used to analyse the relation between lung cancer and cigarette smoking. The model contains the main rate-limiting stages of carcinogenesis, which include initiation, promotion (clonal expansion of initiated cells), malignant transformation and a lag time for tumour formation. Various data sets were used to test the model. These include the data of a large prospective collaborative project carried out in 10 different European countries, the European Prospective Investigation into Cancer and Nutrition (EPIC). This new data set has not been modelled before. The model is also tested on other published data from CPS-II (Cancer Prevention Study II) of the American Cancer Society and the British doctors' study. The analyses indicate that the EPIC data are best described with smoking dependence on the rates of malignant transformation and clonal expansion. With increasing smoking rates, saturation effects in the two exposure rate-dependent model parameters were observed. The results find confirmation in the biological literature, where both mutational effects and promotional effects of cigarette smoke are documented.