Ascending thoracic aortic aneurysm (ATAA) in patients with bicuspid aortic valve (BAV) can present an asymmetrical aortic dilatation compared with patients with tricuspid aortic valve (TAV). This pattern of aneurysm dilatation led us to hypothesize that biomechanical differences likely induced by regional heterogeneity of material properties can underlie the observed asymmetric enlargement discrepancies between BAV ATAA and TAV ATAA. This study aimed to characterize the mechanical properties and associated aortic tissue stiffness changes along the circumferential direction of aortic rings collected from surgically-repaired patients with ATAA. Biaxial material testing was performed on tissue specimens extrapolated from all aortic quadrants (i.e. anterior, posterior, major and minor curvature of the aorta), and then the tissue stiffness was quantified at both physiological and supra-physiological stress levels (i.e. 142 kPa and 242 kPa, respectively). Tissue stiffness revealed that the major curvature of BAV ATAA is statistically less stiff than the anterior quadrant (276.6 +/- 137.1 kPa for BAV ATAA and 830.1 +/- 557.1 kPa for BAV ATAA, p = .024, at 142 kPa) and to that of major curvature of TAV ATAA (276.6 +/- 137.0 kPa for BAV ATAA and 733.2 +/- 391.1 kPa for TAV ATAA, p = .001, at 142 kPa), suggesting local weakening of bicuspid aortic wall. Multiphoton imaging revealed local changes on elastic fiber networks. The recovered material parameters for the Fung-type constitutive model are crucial for reliable stress predictions while the information on regional tissue stiffness changes are fundamental to develop risk stratification strategies not based on aortic size.