To ensure the reliability of ultrasonic nondestructive testing techniques for modern structural materials, the effects of anisotropy and inhomogeneity and the influence of non-planar component geometries on ultrasonic wave propagation have to be taken into account. In this article, fundamentals and applications of two analytical approaches to three-dimensional elastic beam field calculation are presented. Results for both isotropic materials including curved interfaces and for anisotropic media like composites are presented, covering field profiles for various types of transducers and the modeling of time-dependent rf-signals.