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Experiences from isotropic materials suggest that it is impossible to derive a statistical model with few parameters to model a weld in an anisotropic material. The parameter that remains unknown even after a large number of empirical investigations is the orientation of the dendrites due to the heating. Our intention is to apply some simplified models in an optimization scheme to predict the dendrites orientation in different kinds of welds. In this paper, a model of ultrasonic ray traveling through anisotropic materials, as well as the corresponding computer simulation is presented. First, based on the previous work on texture analysis of various austenitic stainless steel weld samples, a typical simplified model of the geometry of welds is established. It is subdivided into a finite number of smaller regions with specific anisotropy. Then by means of the ray tracing method, ray path running through the weld model is developed. As a function of incident angle, the point of entrance of the sound path to the weld and the given orientation of the dendrites, the model will ultimately give the point where the sound leaves the weld, the time of flight and the angle between the sound ray and the weld. A numerical simulation of the forward problem is also provided as a validation of the model.