The health effects of inhaled fibers are related to the intensity and duration of exposure and occur many years after the exposure. In particular, the incidence of mesothelioma after exposure to asbestos is proportional to the intensity of exposure (fibers per milliliter of air) and the duration of exposure, and to the time that has elapsed since the exposure. The incidence increases with time since exposure to a power of between 3 and 4. The disease process resulting from exposure to fibers in the air is presumably related to the dose of fibers in the lungs, which depends on the exposure level and duration, and also on the size characteristics of the fibers influencing their inhalation and retention in the lungs. Models incorporating these characteristics have been found to be satisfactory in explaining the incidence of mesothelioma over time after exposure to asbestos. Most of the epidemiological modeling has been for occupational exposure to one of the amphibole asbestos types (crocidolite or amosite), for which heavy exposure produces a high incidence of mesothelioma. Occupational exposure to chrysotile asbestos has resulted in a much lower incidence of mesothelioma. Crocidolite asbestos is much more biopersistent than chrysotile asbestos in the sense that after retention in the lungs it is eliminated only slowly (half-time of several years). If fibers are eliminated then the dose in the lungs declines following exposure, and this may influence the disease process. This concept is more important for synthetic mineral fibers, such as glass wool, which are used as a substitute for asbestos. These fibers are much less biopersistent than asbestos, with half-times of weeks or even days. Biopersistence is related to the dissolution of fibers. This is a physical-chemical process that may be expected to proceed at about the same rate in rats and humans. The predicted effect of biopersistence of fibers has been explored using the basic mesothelioma incidence model generalized to include a term representing exponential elimination over time. The influence of solubility of fibers on the mesothelioma rate is 17 times higher in humans than in rats. This is because rats are aging and developing cancer at a much quicker rate than humans, and hence the influence of dissolution is less. Thus, the predicted mesothelioma incidence in humans is highly dependent on the rate of elimination across the range covering asbestos and the more durable synthetic fibers, but in rats a similar dependence occurs at a 17 times higher rate of elimination corresponding to the less durable synthetic fibers. The possible carcinogenic effects of fibers are often determined from animal experiments, but these results suggest that the extrapolation from rats to humans is highly dependent on the biopersistence of fibers, in the situation where the elimination is through dissolution of fibers at a rate independent of species and the speed of the cancer process is species dependent. This implies that relatively soluble fibers that do not produce disease in rat experiments are even less likely to produce disease in humans.