We analyzed mesothelioma incidence in the Surveillance, Epidemiology, and End Results (SEER) database over the period 1973-2005 using extensions of the age-period-cohort (APC) models. In these analyses, the usual non-specific age effects of the conventional APC models were replaced by hazard functions derived from two multistage models of carcinogenesis, the Armitage-Doll model and the two-stage clonal expansion (TSCE) model. The extended APC models described the incidence data on pleural and peritoneal mesotheliomas well. After adjustment for temporal trends, the data suggest that the age-specific incidence rates of both pleural and peritoneal mesotheliomas are identical in men and women. Driven largely by birth cohort effects, age-adjusted rates of pleural mesothelioma among men rose from about 7.5 per million person-years in 1973 to about 20 per million person-years in the early 1990s and appear to be stable or declining thereafter. Age-adjusted rates of pleural mesothelioma among women have remained more or less constant at about 2.5 per million person-years over the period 1973-2005. Age-adjusted rates for peritoneal mesothelioma in both men (1.2 per million person-years) and women (0.8 per million person-years) exhibit no temporal trends over the period of the study. We estimate that approximately 94,000 cases of pleural and 15,000 cases of peritoneal mesothelioma will occur in the US over the period 2005-2050.