Inversion of surface wave velocities in examples of multilayered anisotropic media is examined using an extension of the Smith-Dahlen formulation. Thus, surface wave propagation in a slightly anisotropic earth model has been found and the inversion of the azimuthal dependence of surface wave dispersion curves has been performed. The inversion scheme proposed in this paper has been verified by numerical matrix inversion with a computer programme in FORTRAN code. In two examples, hexagonal simmetry and 13 non zero canonical harmonic components, we have got results that show an excellent agreement between all phase velocities obtained for both Love and Rayleigh waves. We also perform two additional experiments with observed data, Love and Rayleigh waves phase velocities results of previous studies carry out in the Pacific (Nishimura & Forsyth, 1985, 1988, 1989). In these data test we also have a good agreement between observed and theoretical data.