Three types of transducer beam models are developed for obtaining the bulk waves generated by a plane piston transducer radiating through a planar fluid-solid interface. The first type, called the surface integral model, is based on a Rayleigh-Sommerfeld-like integral that requires a two-dimensional surface integral to be evaluated. The second model, called the boundary diffraction wave (BDW) paraxial model, simplifies the two-dimensional integration of the surface integral model to a one-dimensional line integration. The third type of model, called the edge element model, is shown to be a novel way of efficiently evaluating the two-dimensional surface integration of the surface integral model. The limitations of these models for simulating inspections near critical refracted angles and near the interface are discussed. It is shown that the introduction of the paraxial approximation in the BDW model allows that model to be computed with a very large (300-1) speed advantage over the surface integral while retaining the same accuracy in most cases. The edge element model, while having a smaller (5-1) advantage over the direct numerical integration of the surface integral model, retains the accuracy of the surface integral model in cases where the paraxial approximation fails and can be easily generalized to more complex testing situations (focused probes, curved interfaces, etc.).