Ultrasonic Non Destructive Testing can be heavily affected by heterogeneous materials, such as some coarse-grained metals, concretes or composites materials. Understanding and predicting the behaviour of ultrasonic waves in such complex media has been a longstanding focus of research. Originally, theoretical analytical models have been developed. Their utility tend to be constrained by their inherent approximations and by the difficulties associated with verifying them. In recent years, transient Finite Element computations have been used to overcome these limitations. By simulating the propagation of ultrasonic waves through representative volumes of the material, it is possible to determine the properties of the coherent wave. However, this approach has been mainly applied to longitudinal waves only, and the analysis methods used are not necessarily applicable to shear waves. This communications shows how, with a dedicated simulation setup, it is possible to characterize the behaviour of both longitudinal and shear waves. Both waves can be characterized using a single computation, saving on computation times. The presented methodology is also applicable to statistically anisotropic medias, such as textured metallic microstructures, in which three distinct modes can be observed in the coherent field: one quasi-longitudinal and two quasi-shear modes. These three modes can be characterized in a single simulation. One of the objectives of this technique is to provide material input data for ray-based macroscale simulations using ray-based or high order Finite Element models in application to the control of various metallic parts, including welded components with textured regions.