Rapid exit taxiways enhance runway operational capacities by means of reducing the runway occupancy times of aircraft. The selection of rapid exit taxiway locations is important to achieve the optimum runway capacity. This paper presents a methodology for locating rapid exits based on excursion risk. Considering the level of severity and frequency of historical runway-related accidents and emerging use of rapid exit taxiways in the future, this study explores the associated veer-off risk at rapid exits. The proposed methodology estimates veer-off risk using three successive steps such as event probability, location probability, and severity estimation. An existing logistic regression model developed for landing overrun probability estimation is adapted for the exit taxiway facility to estimate event probability. Aircraft touchdown speed, deceleration, and runway criticality factor are the important operational parameters of this model adaptation. The aircraft turn path radius and kinetic energy at the time of veer-off are used to estimate the respective location probabilities and accident severities. As the sample analysis proves, the associated veer-off risk increases when the exits are closer to the runway threshold. The paper recommends wider taxiways and larger taxiway radii to compensate for increasing veer risks. The methodology helps for planning risk-based rapid exit taxiways for varying design, operational, and weather conditions.