Rupture of abdominal aortic aneurysm (AAA) represents a significant clinical event, having a mortality rate of 90% and being currently ranked as the 13th leading cause of death in the US. The ability to reliably evaluate the susceptibility of a particular AAA to rupture on a case-specific basis could vastly improve the clinical management of these patients. Because AAA rupture represents a mechanical failure of the degenerated aortic wall, biomechanical considerations are important to understand this process and to improve our predictions of its occurrence. Presented here is an overview of research to date related to the biomechanics of AAA rupture. This includes a summary of results related to ex vivo and in vivo mechanical testing, noninvasive AAA wall stress estimations, and potential mechanisms of AAA wall weakening. We conclude with a demonstration of a biomechanics-based approach to predicting AAA rupture on a patient-specific basis, which may ultimately prove to be superior to the widely and currently used maximum diameter criterion.