Abstract: This study investigates the anisotropy of wave velocities of granular materials from both macroscopic and microscopic scales. The effects of stress states on the P- and S-wave velocities propagating along multiple directions in granular samples of PVC particles are examined in a cylindrical torsion-shear apparatus with two bender elements. Using X-ray computed tomography, the fabric evolution of the specimen, including the coordination number, particle orientation and contact normal, during consolidation along different stress paths is analyzed. The results indicate that an initial stiffness anisotropy can be observed that the horizontal stiffness of the specimen is larger than that in the vertical direction, which is related to the particle long axes distribution. As the ratio of vertical to horizontal stress increases, the wave velocity along the vertical direction increases, while the horizontal wave velocity remains nearly constant before an obvious decrease. This trend is strongly associated with the variation of coordination number. Moreover, the ratio of vertical to horizontal stress-normalized wave velocity keeps almost unchanged and then gradually approaches to 1.0 as the stress ratio increases, which is related to the evolution of particle long axes and contact normal based fabric anisotropy.