Modern structural materials mostly exhibit anisotropic elastic behavior len
ding to complicated wave propagation phenomena. To ensure the reliability o
f ultrasonic nondestructive testing techniques, these material properties,
as well as the influence of microstructural inhomogeneities and the effects
of nonplanar surfaces and interfaces on ultrasonic wave propagation, have
to be taken into account. In this respect, mathematical modeling provides a
n efficient method of assisting analysis. This paper presents two analytica
l approaches that are well suited for performing ultrasonic wave propagatio
n and scattering simulations for complex structured media on a personal com
puter. Results for both isotropic materials, including curved interfaces, a
nd for anisotropic media, such as composites and weld material, are present
ed. The simulation of transducer field profiles, the propagation of time de
pendent rf signals and the scattering of ultrasound at discontinuities are
addressed.