A procedure is presented that expresses pollutant movement in groundwater as a probability distribution. Probability is introduced into the pollutant movement solution process by using the Turning Bands Method (TBM), a spectral analysis model. The TBM generates a selected number of spatially-varying, correlated hydraulic conductivity fields, all of which have the same descriptive statistics, i.e., mean, standard deviation and correlation function. A groundwater flow-mass transport model developed by the Illinois State Water Survey is used to predict pollution concentration as a function of space and time for a specified groundwater contamination event. The groundwater flow-mass transport model develops a set of pollution movement estimates, one for each hydraulic conductivity field generated by the TBM. These realizations of pollutant movement are described first as frequency distributions and eventually as cumulative exceedance probability distributions;This procedure is applied to a documented field situation at the Idaho National Engineering Laboratory (INEL). Disposal of tritium in low-level radioactive and chemical wastes from the Idaho Chemical Processing Plant (ICPP) into the Snake River Plain aquifer through a deep injection well was recorded from 1976 through 1982. The movement of the tritium plume has been observed at several monitoring sites. TBM and groundwater flow-mass transport model parameters are determined in a calibration process with the recorded INEL data. One hundred realizations of a tritium disposal event during 1979 and 1980 at the INEL are used to generate cumulative exceedance probabilities of time of arrival and tritium concentration versus duration of exposure at an observation well downstream of the ICPP injection well;The observed cumulative exceedance probability distributions of time of arrival and conditional and marginal cumulative exceedance probability distributions of each tritium concentration and duration of exposure are fitted to the Pearson Type III distribution. A logit transformation is used to obtain a simple mathematical equation representing the joint cumulative exceedance probability distribution of tritium concentration and duration of exposure. Finally, the pertinence of these types of probability results to toxicity studies and benefit-cost analysis is discussed.