A rail inspection system based on ultrasonic guided waves and non-contact (air-coupled) ultrasound transduction is under development at the University of California at San Diego. The system targets defects in the rail head that are major causes of train accidents. Because of the high acoustic impedance mismatch between air and steel, the non-contact system poses severe challenges and questions on the defect detection performance. This article presents an extensive numerical study, conducted with a local interaction simulation approach, to model the ultrasound propagation and interaction with defects in the proposed system. This model was used to predict the expected detection performance of the system in the presence of various defects of different sizes and positions, and at varying levels of signal-to-noise ratios. When possible, operating variables for the model were chosen consistently with the field test of an experimental prototype that was conducted in 2014. The defect detection performance was evaluated through the computation of receiver operating characteristic curves in terms of probability of detection versus probability of false alarms. The study indicates that despite the challenges of non-contact probing of the rail, quite satisfactory inspection performance can be expected for a variety of defect types, sizes, and positions. Beyond the specific cases examined in this article, this numerical framework can also be used in the future to examine a larger variety of field test conditions.