Case notification data from the U.S. Centers for Disease Control imply that AIDS has spread rapidly among intravenous drug users in the northeastern United States. These data determine a doubling time for AIDS cases of 5-6 months for this population early in the epidemic. A new mathematical model of transmission of human immunodeficiency virus (HIV) via shared drug injection equipment in "shooting galleries" is developed to understand the rapid spread of HIV and AIDS among drug users. The model depends on quantities such as rates of sharing injection equipment, the ratio of addicts to injection equipment in the population, the infectivity of HIV transmitted by shared injection equipment, the likelihood that infectious equipment is "flushed" by the blood of an uninfected user, and the duration of needle-sharing activity by HIV-infected addicts. The model is extended to incorporate the impact of cleansing or bleaching of injection equipment. Also, the model is reformulated to account for the inactivation of HIV infectiousness over time. The models demonstrate that policies such as the distribution of cleansing solutions and/or injection equipment among drug addicts could slow or stop the intravenous transmission of HIV in shooting galleries.