We estimated Rayleigh- and Love-wave group-velocity dispersion curves using dense seismic networks in Saudi Arabia and nearby countries. We merged our data with group- and phase-velocity dispersion curves from previous studies to produce a new isotropic and radially anisotropic S-velocity model for the Arabian plate and nearby regions. Strong negative radial anisotropy (VSH < VSV) is observed in the crustal depth beneath the southern Red Sea, but weak positive radial anisotropy (VSH > VSV) and relatively thick lithosphere are found beneath the northern Red Sea, implying different tectonics between the two regions. We found low-velocity anomalies beneath Cenozoic volcanism in the Arabian Peninsula, but corresponding radial anisotropic perturbations are observed differently in spatiotemporal regimes depending on source origin. From the strong positive radial anisotropy at asthenospheric depth, which correlates with a circular pattern of azimuthal anisotropy from shear-wave splitting, we infer toroidal mantle flow around regions of thick lithosphere including an eastern part of the Arabian platform, the Mesopotamian Plain, and the Zagros belt. On the contrary, weak radial anisotropy is found beneath the thin lithosphere of the Arabian shield and in the thick lithosphere of the Mesopotamian, which may imply vertical flow due to asthenospheric upwelling and cratonic growth, respectively.