A topic of ongoing interest to the manufacturing community is the development of models to simulate ultrasonic (UT) inspections of manufactured parts. In previous work [1] we presented a model approach for predicting the effects of internal flaws upon throughtransmitted UT signals. This approach, which combines Auld’s reciprocity formula and a Kirchhoff approximation, proved very successful in simulating normal-incidence inspections of graphite/composite plates containing seeded delaminations. A key ingredient of our approach is the Gauss-Hermite (GH) model for the propagation of bulk ultrasonic waves in homogeneous media [2,3]. This beam model, in which one expands a time-harmonic displacement field in terms of a truncated set of Gauss-Hermite basis functions, has a number of desirable features. The ultrasonic transducer generating the waves may be planar, focussed, or of unusual design. The expansion coefficients which multiply the basis functions are obtained by numerical integrations over the face of the transducer. Once these transducer-dependent constants have been calculated, displacement fields can be rapidly computed. Paraxial approximations are available which describe how a given expansion function is modified by passage through a planar or curved interface. The use of these approximations makes the model especially well suited for problems in which a beam is being propagated through successive layers of material: computation times are nearly identical for single-layer and multi-layer problems. The layers can be either isotropic or anisotropic in nature, although in the current formulation of the model there are some restrictions on the direction of propagation for anisotropic materials [3]. Because the model employs paraxial approximations it is not appropriate for highly divergent beams, or for beams striking interfaces near the critical angle of incidence.