The ultrasonic detection of cracks in the interior of an elastic solid by the use of surface transducers is a fundamental NDE problem. The presence of cracks may be detected either by observing the back scattered elastic waves using the launching transducer as a receiver or by observing obliquely scattered waves with a separate receiving transducer located elsewhere on the surface. Unfortunately, most of the theoretical work on the scattering of elastic waves from cracks has been confined to the case of a crack in an unbounded elastic solid, a situation far different from the experimental one. Even in that case, exact results are available only for the crack occupying a half plane. Exact results for cracks having finite surface area, such as a penny shaped cracks, are not available in detail, although many approximate calculations have been published, particularly in the low frequency limit
