Hanford, Washington (USA) is the construction site of a multi-billion-dollar high-level nuclear waste treatment facility. This site lies 200 kilometers (km) east of Mount St. Helens (MSH), the most active volcano in the contiguous United States. Tephra from a future MSH eruption could pose a hazard to the air intake and filtration systems at this plant. In this report, we present a probabilistic estimate of the amount of tephra that could fall, and the concentrations of airborne ash that could occur at the Hanford Site during a future eruption. Mount St. Helens has produced four large explosive eruptions in approximately the past 500 years, suggesting that its annual probability of eruption (P₁) is roughly 4/500=0.008. Assuming that a large eruption occurs, we calculate the probability (P_3|1) of a given fall deposit thickness or airborne concentration at Hanford by running about 10,000 simulations of ash-producing eruptions using the atmospheric transport model Ash3d. In each simulation, we calculate the pattern of tephra dispersal, deposit thickness at Hanford, and airborne ash concentration at ground level. As input for each simulation, we choose meteorological conditions from a randomly chosen time in the historical record between 1980 and 2010, using data from the European Centre for Medium-Range Weather Forecasting (ECMWF) Reanalysis (ERA) Interim model. The volume (dense-rock equivalent) of each simulated eruption is randomly chosen from a uniform probability distribution on a log scale from the range of magma volumes (0.008–2.3 cubic kilometers [km³]) estimated for late Holocene eruptions at MSH. Plume heights and durations of each eruption are chosen using empirical correlations between volume, height, and eruption rate, which account for the fact that larger eruptions have higher plumes and last longer. We construct summary tables of final deposit thickness (T), maximum ground-level airborne concentration (C_max), and average ground-level airborne concentration (C_avg) during tephra-fall for each run. Each table is sorted and ranked by decreasing value of T, C_max, or C_avg. Conditional probabilities (P_3|1) are derived by dividing rank by n+1, where n is the total number of successful runs. For example, a deposit thickness of 5.10 centimeters (cm) from run 446 is ranked 123 of 9,785 successful runs, yielding P_3|1=123/9,786=0.01257. Its annual probability is P=P₁·P_3|1=0.008×0.01257=0.000101. By interpolation, the deposit thickness (T_10k) having an annual probability of 1 in 10,000 (P= 0.0001) is 5.11 cm. Analogous concentration values are C_max,10k=3,819 and C_avg,10k=1,513 milligrams per cubic meter (mg/m³), respectively. Independent calculations using the known mass accumulation rate of the deposit (=0.001–0.006 kilograms per square meter per second [kg/m²/s]), aggregate fall velocities (u=0.3–0.8 meters per second [m/s]), and the simple formula , yield similar results, although highly variable fall velocities add significant uncertainty. This formula implies that deposit accumulation rates of millimeters (mm) to greater than 1 cm per hour, which are not uncommon during heavy ash fall, are associated with airborne concentrations of 10²–10³ milligrams per cubic meter (mg/m³). These concentrations are much higher than published measurements (10^-3–10¹ mg/m³), which record only suspended particles sampled in sheltered areas. During heavy ashfall, most fine ash falls as aggregates. Whether such aggregates will be ingested into air ducts will depend on the aggregate size and fall rate, the fragility of the aggregates, the air duct geometry, intake velocity, and other factors.