OBJECTIVE: Mechanical properties of healthy, aneurysmal, and atherosclerotic arterial tissues are essential for assessing the risk of lesion development and rupture. Strain energy density function (SEDF) has been widely used to describe these properties, where material constants of the SEDF are traditionally determined using the ordinary least square (OLS) method. However, the material constants derived using OLS are usually dependent on initial guesses. METHODS: To avoid such dependencies, Bayesian inference-based estimation was used to fit experimental stress-stretch curves of 312 tissue strips from 8 normal aortas, 19 aortic aneurysms, and 21 carotid atherosclerotic plaques to determine the constants, C1, D1, and D2 of the modified Mooney-Rivlin SEDF. RESULTS: Compared with OLS, material constants varied much less with prior in the Bayesian inference-based estimation. Moreover, fitted material constants differed amongst distinct tissue types. Atherosclerotic tissues associated with the biggest D2, an indicator of the rate of increase in stress during stretching, followed by aneurysmal tissues and those from normal aortas. Histological analyses showed that C1 and D2 were associated with elastin content and details of the collagen configuration, specifically, waviness and dispersion, in the structure. CONCLUSION: Bayesian inference-based estimation robustly determines material constants in the modified Mooney-Rivlin SEDF and these constants can reflect the inherent physiological and pathological features of the tissue structure. SIGNIFICANCE: This study suggested a robust procedure to determine the material constants in SEDF and demonstrated that the obtained constants can be used to characterize tissues from different types of lesions, while associating with their inherent microstructures.