For ultrasonic inspection of austenitic welds and cladded components mostly horizontally polarized shear waves and quasi-longitudinal (qP) waves are applied. Depending on the testing situation the one or the other wave type offers certain benefits. To explain experimentally observed phenomena and to predict how qP-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 qP-waves propagating in ideally fiber-textured austenitic weld material. Based on a mild anisotropy approximation given previously by Tverdokhlebov and Rose [1], a direct relationship between wave propagation directions and spatial coordinates has been obtained. This relationship has been applied to the Generalized Point-Source-Synthesis method (GPSS) to model radiation, propagation and scattering effects [2,3]. The GPSS-code thus improved 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 evaluations are presented for both continuous wave and time-dependent rf-impulse modeling for austenitic weld metal specimens, covering field profiles for a normal transducer and for a 32-element phased array probe. For the latter, wavefront images are also shown. The differences in the results obtained with this accelerated modeling code as compared with the exact code are of no practical importance. Further evaluations are shown in [4], where the calculation of three-dimensional transducer fields is considered.