In the western Indian Ocean, the Reunion hot spot is one of the most active volcanoes on Earth. Temporal interactions between ridges and plumes have shaped the structure of the zone. This study investigates the mantle structure using data from the Reunion Hotspot and Upper Mantle-Reunions Unterer Mantel (RHUM-RUM) project, which significantly increased the seismic coverage of the western part of the Indian Ocean. For more than 1year, 57 ocean bottom seismometer stations and 23 temporary land stations were deployed over this area. For each earthquake station path, the Rayleigh wave fundamental mode phase velocities were measured for the periods from 30s to 300s and group velocities for the period from 16s to 250s. A three-dimensional model of the shear velocity in the upper mantle was built in two steps. First, the path mean phase and group velocities were inverted, to obtain regionalized velocity maps for each separate period. Then, all of the phase and group velocity maps were combined and inverted at each grid point, to obtain the local S wave velocity as a function of depth, using a transdimensional inversion scheme. The three-dimensional anisotropic S wave velocity model has resolution down to 300km in depth. The tomographic model and surface tectonics are correlated down to approximate to 100km in depth. Starting at 50km in depth, a slow velocity anomaly beneath Rodrigues Ridge and the east-west orientation of the azimuthal anisotropy show a connection between Reunion upwelling and the Central Indian Ridge. The slow velocity signature beneath La Reunion is connected at greater depths (150-300km) with a large slow velocity zone beneath the entire Mascarene Basin. This develops along a northeast direction, following the general motion direction of the African Plate. These observations indicate nonisotropic spreading of hot plume material and dominant horizontal flow in the upper mantle beneath this area.