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Practical ultrasonic inspection requires modeling tools that enable rapid and accurate visualization; because of the increasing sophistication of practical inspection, it is becoming increasingly difficult to use a single modeling method to represent an entire inspection process. Hybrid models that utilize different or interacting numerical schemes in different regions, to use their relative advantages to maximal effect, are attractive in this context, but are usually custom-made for specific applications or sets of modeling methods. The limitation of hybrid schemes to particular modeling techniques is shown here to be related to their fundamental formulation. As a result, it becomes clear that a formalism to generalize hybrid schemes can be developed: an example of the construction of a generic hybrid modeling interface is given for the abstraction of bulk ultrasonic wave phenomena, common in practical inspection problems. This interface is then adapted to work within a prototype hybrid model consisting of two smaller finite element model-domains, and explicitly demonstrated for bulk ultrasonic wave propagation and scattering examples. Sources of error and ways to improve the accuracy of the interface are also discussed.