For the characterization of soil stiffness anisotropy at small strains and the calculation of soil elastic constants derived from the cross-anisotropic model, it is important to obtain stress wave phase velocities of soils in both principal and oblique directions. This study developed an original eight-prismatic shape apparatus equipped with disk-shaped shear plates to measure shear (S-) wave phase velocities (V-phase) in multiple directions, and four granular materials of various shapes were tested by this apparatus under isotropic confinement. Experimental results confirm the capability of the new apparatus and reveal that both S-wave propagation and oscillation directions are sensitive to soil inner fabric, i.e., V-s changes with the variation of either S-wave propagation or oscillation direction. Based on the experimental observations, it is suggested to keep the same S-wave oscillation direction when measuring V-s in multiple propagation directions so that the corresponding shape of the S-wave surface (polar plots of V-s in arbitrary propagation directions) is more precise to reflect the small-strain stiffness anisotropy of soils.