The doubling of the prison population between 1974 and 1984 led to concern about the need for long-range forecasting and for planning to avoid temporary solutions that might quickly become outmoded. Under a grant from the National Institute of Justice, this study used a computer-based mathematical model to project male prison populations for eight States: Arizona, California, Florida, Illinois, Massachusetts, North Carolina, Pennsylvania, and Utah. The forecasts went through the year 2020. The model used Census Bureau projections, data from the eight States on their current imprisonment policies, and existing criminological theory on the behavior of individual offenders. Concepts of probability from operations research also formed the basis for part of the analysis. Forecasts were made assuming either the maintenance of the status quo in terms of sentencing policy or four possible policy changes. The model showed that prison populations might stop growing by the end of this decade (1989). This would represent a temporary deviation from an upward trend rather than a meaningful trend in itself. However, individual States may show substantial variations from the overall pattern. The growth in prison populations is likely regardless of whether sentencing policies are changed, although increases in average prison terms will place substantial pressures on prison populations. Figures, notes, and a discussion of limitations of forecasts are included.