The NOAA Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT) was evaluated as a research tool to simulate the dispersion and deposition of radioactive fallout from nuclear tests. Model-based estimates of fallout can be valuable for use in the reconstruction of past exposures from nuclear testing, particularly where little historical fallout monitoring data are available. The ability to make reliable predictions about fallout deposition could also have significant importance for nuclear events in the future. We evaluated the accuracy of the HYSPLIT-predicted geographic patterns of deposition by comparing those predictions against known deposition patterns following specific nuclear tests with an emphasis on nuclear weapons tests conducted in the Marshall Islands. We evaluated the ability of the computer code to quantitatively predict the proportion of fallout particles of specific sizes deposited at specific locations as well as their time of transport. In our simulations of fallout from past nuclear tests, historical meteorological data were used from a reanalysis conducted jointly by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR). We used a systematic approach in testing the HYSPLIT model by simulating the release of a range of particle sizes from a range of altitudes and evaluating the number and location of particles deposited. Our findings suggest that the quantity and quality of meteorological data are the most important factors for accurate fallout predictions and that, when satisfactory meteorological input data are used, HYSPLIT can produce relatively accurate deposition patterns and fallout arrival times. Furthermore, when no other measurement data are available, HYSPLIT can be used to indicate whether or not fallout might have occurred at a given location and provide, at minimum, crude quantitative estimates of the magnitude of the deposited activity. A variety of simulations of the deposition of fallout from atmospheric nuclear tests conducted in the Marshall Islands (mid-Pacific), at the Nevada Test Site (U.S.), and at the Semipalatinsk Nuclear Test Site (Kazakhstan) were performed. The results of the Marshall Islands simulations were used in a limited fashion to support the dose reconstruction described in companion papers within this volume.