In order to allow non-destructive characterizations by acoustic microscopy, the materials presenting in their properties a gradient perpendicular to the surface are modelled. The method consists in regarding the material as built of a succession of homogeneous layers numerous enough for the acoustic parameters to vary quasi-continuously. The gradient in Young modulus existing in the material is related to a gradient in acoustic properties measurable by acoustic microscopy. The role of the shape of the gradient profile is taken into account in the study of the convergence of the velocity of the surface mode V S. The dispersion of the velocity V S versus d/λ (d is the depth of the gradient area and λ is the wavelength) is studied as a function of the gradient profile. The shape of the curves shows that the best sensitivity to the profile is obtained for d/λ≈1.