Models of the incubation period of anthrax are important to public health planners because they can be used to predict the delay before outbreaks are detected, the size of an outbreak and the duration of time that persons should remain on antibiotics to prevent disease. The difficulty is that there is little direct data about the incubation period in humans. The objective of this paper is to develop and apply models for the incubation period of anthrax. Mechanistic models that account for the biology of spore clearance and germination are developed based on a competing risks formulation. The models predict that the incubation period distribution depends critically on the rate that spores are cleared from the lung and to a lesser extent on the dose of inhaled spores. The models are used in a statistical analysis of data from an anthrax outbreak that occurred in Sverdlovsk, Russia. The analysis suggests that spores are cleared from the lung at a rate between 8% per day, and 14% per day, which is in good agreement with experimental studies of animals. The analysis suggests that at low doses, the overall median incubation period time is about 10 days, which includes a median lag of about 2 days between spore germination and onset of symptoms. Male gender and younger ages were associated with longer incubation periods as was lower dose of inhaled spores.