Two surface waves can propagate on a solid–fluid interface: the Rayleigh and the Stoneley waves. The problem is well known when the fluid sound velocity cF is lower than the velocities in the solid (cS and cL). The Scholte–Stoneley dispersion equation has been studied when cF is greater than the shear wave velocity cS. The numerical results obtained for PVC–water and PlexiglasR–water show that there might exist two surface waves whose velocities are lower than cS. The two corresponding roots of the dispersion equation tend to the Rayleigh root of the solid–vacuum interface as the density of the fluid tends to zero. The structure of the two waves has been studied using the formalism of the evanescent plane waves. They are theoretically propagating without attenuation along the interface and exponentially decaying along the direction normal to the interface inside both media. These two waves have been experimentally observed. They exponentially decay along the direction normal to the interface inside both media. The experimental arrival times are in very good agreement with the theoretical ones.