Probabilistic models are developed for directional wind speeds in hurricane, thunderstorm, and synoptic wind storms. The models, calibrated to data, are used to generate synthetic directional wind speeds over periods of arbitrary length and to assess the uncertainty in the resulting extreme wind speeds. The procedure for generating data uses MATLAB functions, called dirihurricane, bootstrapipar, and bootstrapiparits, and available on www.nist.gov/wind. The synthetic data generated by the models and MATLAB functions developed in this study provide a rational tool for constructing synthetic directional wind speed data that are statistically consistent with existing wind records. The developments in this study are needed because large sets of synthetic data are required to assess the performance of tall buildings and other structural systems under directional wind speeds.