This study explains processes for the characterization by acoustic microscopy of materials presenting, along a thickness d close to the surface, a gradient in elastic properties in direction perpendicular to the surface. The method, modelling the non-homogeneous area by a finite number of layers of the same thickness, is sensitive to the factor fd (f is the working frequency) and to the nature of the gradient profile. The study of the dispersion of the Rayleigh velocity as a function of frequency shows that the shape of the curve Maynly depends on the gradient profile and on the structure (surface material and bulk material). When the numerical derivative of the dispersion curves presents inflexion points, they can be linked to the depth and to the nature of the profile. Modelling of the materials displaying a gradient shows that, in some cases, the plot of the curvature of the dispersion curves as a function of frequency is a useful means of characterization.