A methodology that has been applied for a relatively short time on Seismology is the modelling of very shallow structures from the inversion of dispersion values (group velocity of short period Rg waves). This is possible, because the very short period Rg wave group velocity is sensitive to the variations in the structure of shear velocity for the shallowest layers of the crust. In this line, we have undertaken in the present work, the determination of the shear velocity models for Andalucia and Alboran Sea region (southern Iberia), by means of the generalized inversion of dispersion curves corresponding to Rg waves (short period Rayleigh waves). We use digital filtering techniques, which provide a significant improvement in the signal-to-noise ratio helping to determine a reasonable model for velocity of shear waves. The dispersion curves obtained shows the complexity of the average structure crossing for the waves in each path analysed. We have inverted the average dispersion curves obtained for every path analysed in order to obtain theoretical shear-velocity models, according to the generalized inversion theory. The results obtained show the existence, in the study area, of strong lateral variations in the physical properties of the materials for a rank of depths between 0 to 5 km. The higher velocity values correspond to paths which crossing older structures, whereas the lower values correspond to the paths crossing younger structures.