In this study, an ultrasonic method for characterizing thin films based on the dispersion of the first Rayleigh mode is presented. The principle of surface acoustic waves (SAW) generation using a broadband transducer and their detection is detailed. It is shown that over a frequency range between 20 MHz and 125 MHz, SAWs are sensitive to fine deposits and the attenuation is reasonable thus enabling measurements over 20 millimeters. The Slant Stack transform used to obtain the experimental dispersion curves with excellent signal-to-noise ratios is then presented and analysed. Finally, four samples of silicon on which gold layers 400 nm, 300 nm, 180 nm, and 50 nm thick had been deposited were characterized. The thicknesses and the elastic parameters of the gold layers and the silicon substrate were obtained from the inversions performed on the experimental dispersion curves. These results show the efficiency of the non-destructive ultrasonic technique associated with a Slant Stack transform before inversion.