We present new evidence for the existence of the Love-Rayleigh discrepancy in the Mediterranean region and constrain the average polarization anisotropic structure of the Mediterranean mantle. We analysed regional Rayleigh and Love waveforms recorded at 3-component broadband seismic stations. None of the 3-component seismograms could be fit with a single 1D isotropic and smooth velocity model. However, satisfactory fits for individual Rayleigh and Love waveforms could often be obtained using realistic 1D velocity models. We used these 1D path-average velocity structures to derive 3D S-velocity models for the Mediterranean region. Our results show that Love waves require higher velocities (about 200 m/s) compared to Rayleigh waves between 30 and 120 km depth. We relate the observed anisotropy to lattice-preferred orientation of crystallographic axes of elastically anisotropic minerals such as olivine.