Ascending thoracic aortic aneurysm (ATAA) has been associated with diminished biomechanical strength and disruption in the collagen fiber microarchitecture. Additionally, the congenital bicuspid aortic valve (BAV) leads to a distinct extracellular matrix structure that may be related to ATAA development at an earlier age than degenerative aneurysms arising in patients with the morphological normal tricuspid aortic valve (TAV). The purpose of this study was to model the fiber-reinforced mechanical response of ATAA specimens from patients with either BAV or TAV. This was achieved by combining image-analysis derived parameters of collagen fiber dispersion and alignment with tensile testing data. Then, numerical simulations were performed to assess the role of anisotropic constitutive formulation on the wall stress distribution of aneurysmal aorta. Results indicate that both BAV ATAA and TAV ATAA have altered collagen fiber architecture in the medial plane of experimentally-dissected aortic tissues when compared to normal ascending aortic specimens. The study findings highlight that differences in the collagen fiber distribution mostly influences the resulting wall stress distribution rather than the peak stress. We conclude that fiber-reinforced constitutive modeling that takes into account the collagen fiber defect inherent to the aneurysmal ascending aorta is paramount for accurate finite element predictions and ultimately for biomechanical-based indicators to reliably distinguish the more from the less 'malignant' ATAAs.