An ascending aortic aneurysm is an often asymptomatic localized dilatation of the aorta. Aortic rupture is a life-threatening event that occurs when the stress on the aortic wall exceeds its mechanical strength. Therefore, patient-specific finite element models could play an important role in estimating the risk of rupture. This requires not only the geometry of the aorta but also the nonlinear anisotropic properties of the tissue. In this study, we presented a methodology to estimate the mechanical properties of the aorta from magnetic resonance imaging (MRI). As a theoretical framework, we used finite element models to which we added noise to simulate clinical data from real patient geometry and different properties of healthy and aneurysmal aortic tissues collected from the literature. The proposed methodology considered the nonlinear properties, the zero pressure geometry, the heart motion, and the external tissue support. In addition, we analyzed the aorta as a homogeneous material and as a heterogeneous model with different properties for the ascending and descending parts. The methodology was also applied to pre-surgical,in vivo MRI data of a patient who underwent surgery during which an aortic wall sample was obtained. The results were compared with those obtained from ex vivo biaxial test of the patient's tissue sample. The methodology showed promising results after successfully recovering the nonlinear anisotropic material properties of all analyzed cases. This study demonstrates that the variable used during the optimization process can affect the result. In particular, variables such as principal strains were found to obtain more realistic materials than the displacement field.