Until today, there is no reliable criterion to predict the risk of rupture of abdominal aortic aneurysms (AAAs), which could help in the final clinical decision. The acceptance of the traditional diameter criterion has led to unnecessary surgical procedures with the subsequent high mortality and morbidity. On the other hand, small aneurysms are known that sometimes are subject to rupture, which could be avoided in the case of an early surgical decision. Thus, it becomes necessary to find new criteria, which can reliably predict the actual risk of rupture of AAAs in the clinical setting. This prediction will certainly be a useful clinical tool in the management of patients with AAAs. According to the biomechanical approach in predicting the risk of aneurysm rupture and to the fundamental principles in cardiovascular mechanics, rupture occurs when the AAA wall stresses exceed the failure strength of the wall. Therefore, it becomes obvious that the knowledge of the distribution of stress on a particular AAA wall would be a good indication of its susceptibility to rupture. A methodology to noninvasively determine the in vivo distribution of stresses on the AAA wall is therefore necessary.