Traumatic rupture of the aorta (TRA) is highly lethal in motor vehicle collisions (MVCs). Human body biomechanical models (HUBMs) show promise as useful tools for better comprehension of the mechanical response and injury mechanism of TRA. However, the prediction accuracy largely depends on its material modeling. This study investigated the performance of the isotropic elastic material constitutive model (Mat_001) and the orthotropic elastic material constitutive model (Mat_002) for predicting aortic dynamic response and injury in blunt side impacts, via simulations against vertical and oblique side impact cadaver tests with previously developed HUBM. The aortic strain response, peak intraluminal pressure, thoracic deflections and injury distributions were compared. It was found that both Mat_001 and Mat_002 could be used to model aortic tissue, but Mat_002 presented more sensitivity to blunt side impacts in terms of strain responses. The thoracic rib cage and internal organs sustained more severe injuries under the oblique left side impact (AIS 5+) than those under the vertical left side impact (AIS 4+), whereas the aortic peri-isthmus exhibited a higher TRA risk in the vertical side impact than that in the oblique side impact, with regard to the peak longitudinal strain. The TRA could result from the aorta’s sudden stretch, and the peak longitudinal strain could be regarded as a main contributing factor to it. This study enhances our understanding of the aortic material modeling and injury mechanisms.