To improve the lateral resolution of the first global 3-dimensional models of seismic wave velocities, regional studies have to be undertaken. The dispersion of Rayleigh waves along 86 paths across the Indian Ocean and surrounding regions is investigated in the period range 40--300 s. The regionalization of group velocity according to the age of the sea floor shows an increase of velocity with age up to 150 s only, similar to the results in the Pacific Ocean. But here, this relationship vanishes more quickly at long period. Therefore the correlation of the deep structure with surface tectonics seems to be shallower in the Indian Ocean than in the Pacific Ocean. A tomographic method is applied to compute the geographical distributions of group velocity and azimuthal anisotropy and then the 3--D structure of S--wave velocity. Horizontal wavelengths of 2000 km for velocity and 3000 km for azimuthal anisotropy distribution can be resolved. Except for the central part of the South East Indian ridge which displays high velocities at all depths, the inversion corroborates a good correlation between lithospheric structure down to 120km and surface tectonics: low velocities along the central and southeast Indian ridges, velociaty increasing with the age of the sea floor, high velocities under African, Indian and Australian shields. At greater depths, the low velocity zones under the Gulf of Aden and the western part of the Southeast Indian ridges hold but the low velocity anomaly of the Central Indian ridge is offset eastward. The low velolcity anomalies suggest uprising material and complex plate boundary.