Prison riots, such as the one at the New Mexico State Prison at Santa Fe, could erupt at any one of the major prisons in the country because of severe overcrowding. Between 1973 and 1981, the State and Federal prison population has increased from 196,000 to more than 314,000 -- the sharpest rise in history. One cause of the increase has been the public's strong reaction to apparent increases in crime and their encouragement of tougher sentences. Another has been the steady emptying of mental hospitals, whose former patients often spill into criminal court. However, corrections administrators and analysts increasingly point to the principal factor as the change being made in procedures for handing out criminal punishment. Many State legislatures are eliminating the discretionary powers of judges and parole boards by mandating minimum prison terms. The results are illustrated at the Indiana State Prison at Michigan City, for example, where about 40 percent of the new prison population is made up of persons convicted of minor crimes and where burglars and rapists are serving 100 percent more time than formerly. By last fall, the State prison population exceeded its own rated capacity figure by 30 percent. In several areas, sentencing alternatives are being reintroduced to reduce populations. In Wilmington, Del., for instance, those convicted of less serious crimes are often fined rather than imprisoned, and in Quincy, Mass., a restitution program which helps offenders find jobs has been established. This program, which is operated in conjunction with the Chamber of Commerce, produces about $200,000 in restitution payments each year for theft, personal injury, or property damage. Some experts believe that a return to discretionary sentencing may be necessary to reduce overcrowding in prisons. Photographs are included. A reference list is not provided.