Ultrasonic inspections of axially symmetric forgings, such as those used in the manufacture of jet engine rotating components, are typically performed on so-called “sonic shapes” which have relatively simple geometries. Formation of these sonic shapes typically requires an additional machining step, so significant cost savings can result if the inspections can be reliably performed on forgings whose shapes more closely resemble those of the final machined components. However, compound curvatures of the component surface will cause complicated focusing of the ultrasonic beam within the part which will change the inspection sensitivity to flaws of interest. Analytical models of ultrasonic inspection in complex shaped parts can be used to predict the new sensitivity.