Ultrasonic waves are strongly influenced by the microstructure of the materials through which they propagate, leading to attenuation, dispersion, and noise. Modeling these effects is essential, particularly in non-destructive testing, where they may either hinder defect detection or provide valuable information about the material. Analytical and numerical models help to better predict and interpret these phenomena. Homogeneous statistical properties are generally assumed in such approaches. In practice, however, microstructures often exhibit significant spatial variations, for instance due to manufacturing processes. Depending on the scale of these variations relative to the wavelength, they may induce either abrupt or gradual changes in effective properties. This PhD aims to establish a theoretical framework that accounts for both microstructural randomness and its spatial variations, in order to propose relevant simulation strategies depending on the scales involved. The approach will first be developed in 1D, then extended to 2D and 3D using tools developed in the laboratory, with numerical and possibly experimental validations.