A precise description of the material is a key point to obtain reliable results when using wave propagation codes. In the case of multipass welds, the material is very difficult to describe due to its anisotropic and heterogeneous properties. Two main advances are presented in the following. The first advance is a model which describes the anisotropy resulting from the metal solidification and thus the model reproduces an anisotropy that is correlated with the grain orientation. The model is called MINA for modelling anisotropy from Notebook of Arc welding. With this kind of material model1ing a good description of the behaviour of the wave propagation is obtained, such as beam deviation or even beam division. But another advance is also necessary to have a good amplitude prediction: a good quantification of the attenuation, particularly due to grain scattering, is also required as far as attenuation exhibits a strong anisotropic behaviour too. Measurement of attenuation is difficult to achieve in anisotropic materials. An experimental approach has been based both on the decomposition of experimental beams into plane waves angular spectra and on the propagation modelling through the anisotropic material via transmission coefficients computed in generally triclinic case. Various examples of results are showed and also some prospects to continue refining numerical simulation of wave propagation.