Shear wave elastography (SWE) is an ultrasound (US) diagnostic method for measuring the stiffness of soft tissues based on generated shear waves (SWs). SWE has been applied to bulk tissues, but in arteries it is still under investigation. Previously performed studies in arteries or arterial phantoms demonstrated the potential of SWE to measure arterial wall stiffness-a relevant marker in prediction of cardiovascular diseases. This study is focused on numerical modelling of SWs in ex vivo equine aortic tissue, yet based on experimental SWE measurements with the tissue dynamically loaded while rotating the US probe to investigate the sensitivity of SWE to the anisotropic structure. A good match with experimental shear wave group speed results was obtained. SWs were sensitive to the orthotropy and nonlinearity of the material. The model also allowed to study the nature of the SWs by performing 2D FFT-based and analytical phase analyses. A good match between numerical group velocities derived using the time-of-flight algorithm and derived from the dispersion curves was found in the cross-sectional and axial arterial views. The complexity of solving analytical equations for nonlinear orthotropic stressed plates was discussed.