Rupture properties of thoracic aortic aneurysms (TAAs) were measured in vitro in a pressure-imposed test to predict the ultimate stress of TAAs from their mechanical behavior in a physiological pressure range. Each quadrilateral (ca. 20 × 20 mm2) specimen of TAAs or porcine thoracic aortas (PTAs) was pressurized from the inner wall until rupture or up to 4500 mmHg, while its deformation was being monitored. In-plane stress σ and strain ε of the specimen were calculated using Laplace’s law and deformations of the markers drawn on the specimen surface, respectively. Ultimate stress σ max and tangent elastic modulus H were determined from the σ–ε curve as its maximum stress and slope, respectively. The tangent elastic modulus H of PTA specimens tended to increase with the increase in σ, while that of TAA specimens tended to reach a plateau in a low-σ region. This tendency was confirmed by fitting a function H = C σ (1 − exp(−σ/τ σ )) to the H−σ relation of specimens: The yielding parameter τ σ was significantly lower in TAAs than PTAs. Furthermore, the logarithm of the parameter τ σ correlated significantly with σ max, for all specimens. These results may indicate that τ σ is one of the candidate indices for rupture risk estimation.