In nuclear power plants, welded components can be tested by ultrasonic non destructive means. Such media have peculiar elastic properties, being anisotropic because of the grain growth in the thermal directions during the solidification process, and being heterogeneous due to the succession of welding layers constituted of disoriented grains. Both properties modify the field radiated by a water (or solid wedge) coupled transducer into this medium, by deviating, distorting and scattering it. In the aim to assist settings and interpretations of ultrasonic tests in these media, the French Atomic Energy Commission (CEA) extends its model for the field radiated by arbitrary immersed transducers Champ-Sons [1] to such cases. This paper presents the derivation of the theoretical model for predicting the radiation into an arbitrary anisotropic homogeneous medium. The extension is derived by an asymptotic expansion nearby stationary phase points of an integral expressing the refracted angular spectrum (geometrical optics (GO) approximation). Such a method has proved to ensure both computing efficiency and accuracy, when applied to the case of isotropic medium [2]. Specific developments are required in the neighborhood of caustics (directions of higher intensity), for which the asymptotic expansion is performed to a higher order. Since NDT transducers are mostly wideband, an analytical Fourier transformation allows one to express the field in terms of a time dependent impulse-response.