Ascending thoracic aortic aneurysms (ATAAs) are focal dilatations in the aorta that are prone to rupture or dissect. Currently, the clinically used indicator of the rupture risk is the diameter. However, it has been demonstrated that the diameter alone may not properly predict the risk. To evaluate the rupture risk, one must look into the local mechanical conditions at the rupture site and understand how rupture is triggered in the tissue which is a layered fibrous media. A challenge facing experimental studies of ATAA rupture is that the ATAA tissue is highly heterogeneous; experimental protocols that operate under the premise of tissue homogeneity will have difficulty delineating the heterogeneous properties. In general, rupture initiates at the location where the micro-structure starts to break down and consequently, it is more meaningful to investigate the local conditions at the rupture site. In this work, a combined experimental and computational method was developed and employed to characterize wall stress, strain, and property distributions in harvested ATAA samples to a sub-millimeter resolution. The results show that all tested samples exhibit a significant degree of heterogeneous in their mechanical properties. Large inter-subject variability is also observed. A heterogeneous anisotropic finite strain hyperelastic model was introduced to describe the tissue; the distributions of the material parameters were identified. The elastic energy stored in the tissue was computed. It was found that the tissue fractures preferentially in the direction of the highest stiffness, generating orifices that are locally transverse to the peak stiffness direction. The rupture appears to initiate at the position absorbed of the highest energy. Machine learning was used to classify the curves at rupture and non-rupture locations. Features including material properties and curve geometric characteristics were used. The work showed that the rupture and non-rupture states can indeed be classified using pre-rupture response features. Support vector machine(SVM) and random forest algorithm was employed to provide insight on the importance of the features. Inspired by the importance scores provided by random forest, the rupture groups were interrogated and some strong correlations between the strength and the response features were revealed. In particular, it was found that the strength correlates strongly with the tension at the point where the curvature of the total tension strain curve attains maximum, which occurs early in the response.