Despite the anisotropy of myocardium, previous cardiac MR elastography studies have investigated isotropic stiffness of heart tissue. Anisotropic material properties could provide a better understanding of structural changes that occur in the heart due to pathologies such as diastolic heart failure. However, optimal imaging parameters to measure anisotropic properties are yet unknown. This study investigates the optimal loading frequency that accurately recovers anisotropic stiffness measurements using simulations of cardiac MR elastography experiments in the presence of Gaussian noise and known fibre orientations. The optimised virtual fields method is used as an inversion method to translate harmonic displacements to stiffness parameters.