In ultrasonic nondestructive testing use is made of the physical properties of elastic waves in solids in order to detect defects and material inhomogeneities. Difficulties in testing anisotropic materials are due to the direction dependence of the ultrasonic velocities and to the inherent effects of beam divergence and beam distortion. Based on a theory of elastic wave propagation in transversely isotropic media [1], the Generalized Point-Source-Synthesis-method (GPSS) has been developed to model the radiation, propagation and scattering of elastic waves as generated by ultrasonic transducers in these media [2]. The method accounts for the three-dimensionality and the vectorial character of anisotropic wave phenomena and is particularly useful in view of application-directed modeling at low computation times. A specifically interesting outcome is OPoSSM (‘Optimization by Point-Source-Synthesis-Modeling’), which allows optimized dimensioning and build-up of complex transducers according to their selected field of application. In this contribution, results are presented for austenitic weld material and fiber composites, covering echo dynamic curves — in comparison with experimental results — for commercial transducers. Furthermore, OPoSSM-results on optimized TR-array-probes are presented as well as snapshots of transducer-generated wavefronts, impressively illustrating the modeling of time-dependent rf-signals.