The Kirchhoff approximation is used extensively in modeling ultrasonic scattering by cracks, due to its conceptual simplicity and effectiveness in predicting scattering responses when the crack is favorably oriented. However, when the crack is unfavorably oriented, the Kirchhoff approximation can yield results with unacceptably large errors, due to an incomplete description of waves generated by diffraction at the crack tips. In such circumstances, it is desired to supplement Kirchhoff results with corrections that more accurately predict crack tip diffraction responses. One established means of obtaining such corrections is through application of the “geometrical theory of diffraction” (GTD). While the principles of GTD are appropriate for the problem at hand, implementation of these principles can be problematic when considering cracks with arbitrarily curved edges, due to local failings of various asymptotic assumptions. The goal of the work presented here is to develop a robust approach for applying the underlying principles of GTD to cracks having arbitrarily curved edges, suitable for implementation in an automated algorithm requiring no user intervention.