In vivo quantification of the anisotropic shear elasticity of soft tissue is an appealing objective of elastography techniques because elastic anisotropy can potentially provide specific information about structural alterations in diseased tissue. Here a method is introduced and applied to MR elastography (MRE) of skeletal muscle. With this method one can elucidate anisotropy by means of two shear moduli (one parallel and one perpendicular to the muscle fiber direction). The technique is based on group velocity inversion applied to bulk shear waves, which is achieved by an automatic analysis of wave-phase gradients on a spatiotemporal scale. The shear moduli are then accessed by analyzing the directional dependence of the shear wave speed using analytic expressions of group velocities in k-space, which are numerically mapped to real space. The method is demonstrated by MRE experiments on the biceps muscle of five volunteers, resulting in 5.5 ± 0.9 kPa and 29.3 ± 6.2 kPa (P < 0.05) for the medians of the perpendicular and parallel shear moduli, respectively. The proposed technique combines fast steady-state free precession (SSFP) MRE experiments and fully automated processing of anisotropic wave data, and is thus an interesting MRI modality for aiding clinical diagnosis. Magn Reson Med, 2006. © 2006 Wiley-Liss, Inc.