THE RELATIONSHIP BETWEEN PRISON POPULATIONS AND PRISON CAPACITIES CAN BE AFFECTED BY A VARIETY OF POLICY DECISIONS. FOR EXAMPLE, PROACTIVE POLICY ATTEMPTS TO PLAN PRISON CAPACITY ACCORDING TO PROJECTED PRISON POPULATION INCREASES UNDER THE ASSUMPTION THAT SENTENCING PATTERNS WILL NOT CHANGE SIGNIFICANTLY. REACTIVE POLICY EXPANDS CAPACITY ONLY WHEN COMPLAINTS OF OVERCROWDING ARISE. A THIRD POLICY TENDS TO ADJUST SENTENCING PRACTICE AND PAROLE DECISIONMAKING TO EXISTING PRISON CAPACITY. THE THIRD POLICY IMPLIES THAT IF PRISON SPACE EXISTS, SENTENCING AND PAROLE DECISIONS WILL OPERATE TO FILL THAT SPACE; WHEREAS, IF SPACE DOES NOT EXIST, LIMITED INCARCERATION AND ALTERNATIVES TO INCARCERATION WILL BE DEVELOPED. IN ORDER TO DEVELOP MATHEMATICAL MODELS FOR DEPICTING THE RELATIONSHIPS BETWEEN PRISON POPULATIONS AND PRISON CAPACITY, DATA WERE GATHERED ON THE OPENING OF PRISONS IN EVERY STATE IN EACH YEAR FROM 1955 TO 1976. THE NUMBER OF INMATES IN EACH STATE'S PRISON SYSTEM AT THE END OF EACH YEAR IS ALSO DETERMINED. AN ANALYSIS IS THEN DESIGNED WHICH PERMITS A DESCRIPTION OF THE INTERRELATIONSHIP IN CHANGES OF POPULATION AND CAPACITY ACROSS THESE 1,100 STATE-YEARS OF DATA. A MECHANISM FOR QUANTIFYING THE ISSUES IS DEVELOPED, AND PRELIMINARY STATISTICAL RESULTS AND IMPLICATIONS ARE PRESENTED. TENTATIVE RESULTS INDICATE THAT A LACK OF PHYSICAL CAPACITY CONTROLS INMATE POPULATIONS AND THAT, WHEN PRISONS ARE BUILT, INMATES ARE SENTENCED TO FILL THEM. THE EQUATIONS DEVELOPED ARE DEPICTED. (RCB)