Inversion of teleseismic P wave travel time residuals collected along a 1280-km-long profile traversing the Baikal rift zone (BRZ) reveals the existence of an upwarped lithosphere/asthenosphere interface, which causes a travel time delay of about 1 s at the rift axis (central high). An area with early arrivals relative to the stable Siberian platform of up to 0.5 s is observed on each side of the rift, about 200 km from the rift axis (flank lows). While the location of the central high is approximately fixed in the vicinity of the rift axis, those of the flank lows vary as much as 200 km with the azimuth of the arriving rays. We use three techniques to invert the travel time residuals for velocity anomalies beneath the profile. Two of the techniques assume an isotropic velocity structure, and one of them considers a transversely isotropic velocity model with a vertical axis of symmetry. We use independent geophysical observations such as gravity, active source seismic exploration, and crustal thickness measurements to compare the applicability of the models. Other types of geophysical measurements suggest that the model involving transverse isotropy is a plausible one, which suggests that the central high and flank lows are caused by the combined effects of an upwarped asthenosphere with a 2.5% lateral velocity reduction, and a velocity increase due to transverse isotropy with a vertical axis of symmetry. We consider the anisotropy to be the result of the vertical component of a lithosphere/asthenosphere small-scale mantle convection system that is associated with the rifting.