Some 1,976 sites at closed military bases in the United States are contaminated with unexploded ordnance (UXO) left over from live-fire weapons training. These sites present risks to civilians who might come into contact with the UXO and cause it to explode. This paper presents the first systems analysis model for assessing the explosion risks of UXO at former military training ranges. We develop a stochastic model for estimating the probability of exposure to and explosion of UXO, before and after site cleanup. An application of the model to a 310-acre parcel at Fort Ord, California, shows that substantial risk can remain even after a site is declared clean. We estimate that risk to individual construction workers of encountering UXO that explodes would range from 4 x 10(-4) to 5 x 10(-2), depending on model assumptions, well above typical Occupational Safety and Health Administration (OSHA) and U.S. Environmental Protection Agency (EPA) target risk levels of 10(-4) to 10(-6). In contrast, a qualitative UXO risk assessment method, the Munitions and Explosives of Concern Hazard Assessment (MEC HA), developed by an interagency work group led by the EPA, indicates that the explosion risk at the case study site is low and "compatible with current and determined or reasonably anticipated future risk." We argue that a quantitative approach, like that illustrated in this paper, is necessary to provide a more complete picture of risks and the opportunities for risk reduction.