Ascending thoracic aortic aneurysms (ATAA) have a high propensity for dissection, which occurs when the hemodynamic load exceeds the mechanical strength of the aortic media. Despite our recognition of this essential fact, the complex architecture of the media has made a predictive model of medial failure—even in the relatively simple case of the healthy vessel—difficult to achieve. As a first step towards a general model of ATAA failure, we characterized the mechanical behavior of healthy ascending thoracic aorta (ATA) media using uniaxial stretch-to-failure in both circumferential (n = 11) and axial (n = 11) orientations and equibiaxial extensions (n = 9). Both experiments demonstrated anisotropy, with higher tensile strength in the circumferential direction (2510 ± 439.3 kPa) compared to the axial direction (750 ± 102.6 kPa) for the uniaxial tests, and a ratio of 1.44 between the peak circumferential and axial loads in equibiaxial extension. Uniaxial tests for both orientations showed macroscopic tissue failure at a stretch of 1.9. A multiscale computational model, consisting of a realistically aligned interconnected fiber network in parallel with a neo-Hookean solid, was used to describe the data; failure was modeled at the fiber level, with an individual fiber failing when stretched beyond a critical threshold. The best-fit model results were within the 95% confidence intervals for uniaxial and biaxial experiments, including both prefailure and failure, and were consistent with properties of the components of the ATA media.