The proposed, stochastic model is predicated on the assumption that the overwhelming bulk of crime and imprisonment is associated with chronic offenders. Initially, focus is on the individual chronic offender and the probability that he or she is in prison at a given age. By aggregating over the entire criminal class, an estimate of the total prison population can be obtained. After a validation exercise using Pennsylvania data, the model is used to make illustrative prison population projections about Massachusetts, Utah, and Florida. The results suggest that, while prison populations might stablize everywhere during the early 1990's, only rarely will this situation signify an end to the growth in prison capacity requirements. 3 tables and 15 references. (Author abstract modified)