For ultrasonic inspection of austenitic welds and cladded components horizontally polarized shear (SH) waves — as generated by electromagnetic acoustic transducers (EMATs) — have certain benefits compared with quasi-vertically polarized shear and quasi-pressure waves. SH-waves suffer the least distortion of all three wave modes when propagated through anisotropic weld material and no energy is lost through mode conversion at the steel/free surface or base metal/weld interfaces. To explain experimentally observed phenomena and to predict the cases where SH-waves might be best employed, modeling of the respective wave propagation effects is useful. In this contribution, a computationally efficient modeling code is presented for SH-waves propagating in transversely isotropic media, thus particularly applicable to ideally fiber-textured austenitic weld material. An explicit space-time domain far-field representation of Green’s dyadic function has been derived with respect to the wave type under concern, the fiber direction being included as a free parameter. The obtained relationships have been applied to the Generalized Point-Source-Synthesis method (GPSS [1,2]) to model radiation, propagation and scattering effects. The code thus improved — SH-GPSS— is characterized by a considerable reduction of computer run-time and is therefore particularly convenient in view of a respective extension to inhomogeneous weldments. Numerical results are presented for both continuous wave and time-dependent rf-impulse modeling for austenitic weld metal specimens, covering field profiles as well as wave front snapshots for a phased array EMAT-probe.