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In ultrasonic nondestructive testing (NDT) use is made of the physical properties of elastic waves in solids in order to detect defects and material inhomogeneities. However, modern structural materials mostly exhibit anisotropic elastic behavior leading to complicated wave propagation phenomena. To ensure the reliability of ultrasonic inspection techniques, these material properties as well as the influence of microstructural inhomogeneities and the effects of non-planar surfaces and interfaces on ultrasonic wave propagation have to be taken into account. In this respect, simulation and optimization in ultrasonic testing have gained a considerable importance, where mathematical modeling provides a simple method of assisting analysis. This presentation gives an overview of different analytical approaches to model elastic wave propagation in complex-structured media. Results for both isotropic materials including curved interfaces and for anisotropic media like composites and weld material are presented, covering field profiles for various types of transducers. Modeling of time-dependent RF-signals and the scattering of ultrasound at defects are also addressed.