This report is a part of the John A. Volpe National Transportation Systems Center's Track Stability Research Program for the Federal Railroad Administration on thermal buckling of continuous welded rail (CWR) track and its prevention. Presented in this report are the developments of theoretical results and the development and application of the CWR-SAFE computer software model for prediction of CWR track buckling strength. This comprehensive predictive model encompasses several different modules designed to perform both deterministic and probabilistic buckling analyses, based on the dynamic buckling theory previously validated by tests, and predicts safe limits for buckling prevention. The model accounts for all the important parameters influencing track buckling, such as rail size, curvature, lateral resistance, tie- ballast friction, fastener torsional and longitudinal resistances, track vertical stiffness, misalignment amplitude and wavelength, and vehicle parameters. Applications of the model are demonstrated through analyses of parametric sensitivity, development of buckling safety limits in terms of safe and critical temperatures, and evaluation of annual probability of buckling occurrences for typical CWR line segments. The report also presents techniques to determine the input parameters for CWR-SAFE application and a practical methodology for CWR track safety monitoring. A risk-based approach is proposed to provide more flexibility to the industry in achieving a minimum number of annual buckles in a given territory and to provide science-based guidelines for improved slow order policies when operating at elevated rail temperatures.