Due to their structure and composition, many biological tissues have been shown to be anisotropic. MRE, a non-invasive tool used to measure the stiffness of tissue, has previously been used to diagnose and track disease progression based on tissue stiffness changes. This work presents a robust and novel method for estimating anisotropic stiffness utilising harmonic displacements from MRE and material orientations from DTI. The method was verified using in silico experiments and applied to in vivo imaging data of the lower leg muscles in volunteers. In vivo stiffness estimates show changes in anisotropic stiffness with changes in passive muscle stretch.