In unconsolidated granular media, the state of stress has a major effect on the elastic properties and wave velocities. Effective media modeling of granular packs shows that a vertically oriented uniaxial state of stress induces vertical transverse isotropy (VTI), characterized by five independent elastic parameters. The Rayleigh wave velocity is sensitive to four of these five VTI parameters. We have developed an anisotropic Rayleigh wave inversion that solves for four of the five independent VTI elastic parameters using anisotropic Thomson-Haskell matrix equations that can be used to determine the degree of anisotropy and the state of stress in granular media. The proposed method incorporates an initial model search guided by rock-physics models and dispersion curve inversion that uses a gradient-based solver. We carried out the inversion on a synthetic example and a real data set in which we inverted for in situ elastic moduli of unconsolidated sands at very low effective stress. The synthetic data example results showed that we are able to correctly estimate the granular media’s effective elastic moduli. When the inversion was carried out with real data, the results indicate that the sand at very low effective stress is elastically anisotropic and that it is stiffer along the vertical axis than the horizontal axis. Furthermore, our results are in agreement with past studies related to granular media.