Thoracic aortic aneurysms are life-threatening lesions that afflict young and old individuals alike. They frequently associate with genetic mutations and are characterized by reduced elastic fibre integrity, dysfunctional smooth muscle cells, improperly remodelled collagen and pooled mucoid material. There is a pressing need to understand better the compromised structural integrity of the aorta that results from these genetic mutations and renders the wall vulnerable to dilatation, dissection or rupture. In this paper, we compare the biaxial mechanical properties of the ascending aorta from 10 murine models: wild-type controls, acute elastase-treated, and eight models with genetic mutations affecting extracellular matrix proteins, transmembrane receptors, cytoskeletal proteins, or intracellular signalling molecules. Collectively, our data for these diverse mouse models suggest that reduced mechanical functionality, as indicated by a decreased elastic energy storage capability or reduced distensibility, does not predispose to aneurysms. Rather, despite normal or lower than normal circumferential and axial wall stresses, it appears that intramural cells in the ascending aorta of mice prone to aneurysms are unable to maintain or restore the intrinsic circumferential material stiffness, which may render the wall biomechanically vulnerable to continued dilatation and possible rupture. This finding is consistent with an underlying dysfunctional mechanosensing or mechanoregulation of the extracellular matrix, which normally endows the wall with both appropriate compliance and sufficient strength.