In circumstances where multi-layered structures play a critical role in the performance of manufactured components, a thorough and detailed inspection procedure is required. However the construction of such objects is such that it is not easy to provide an adequate non-destructive test to monitor the state of the structure. It is possible to employ x-ray techniques, but on these layered (or cylindrically symmetric) structures many exposures are required over a range of positions, which is both expensive and time consuming. It is therefore attractive to use an ultrasonic NDT system. A further important motivation for using ultrasound is its sensitivity to a large number of material parameters.