This study explains processes for the characterization by acoustic microscopy of materials presenting, along a thickness d close to the surface, agradient 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 natureof the gradient profile. The study of the dispersion of the Rayleigh velocity as afunction of frequency shows that the shape of the curve Maynly depends on the gradientprofile and on the structure (surface material and bulk material). When the numericalderivative of the dispersion curves presents inflexion points, they can be linked tothe depth and to the nature of the profile. Modelling of the materials displaying agradient shows that, in some cases, the plot of the curvature of the dispersion curvesas a function of frequency is a useful means of characterization.