An abdominal aortic aneurysm (AAA) is a vascular pathology associated with localized and balloon-like dilatations of abdominal aorta. An untreated AAA may lead to an eventual rupture with a high mortality rate. In recent studies, the biomechanics of AAA has been widely used to assess the rupture risk in clinic. In this review paper, biomechanical testing methods on intraluminal thrombi and AAA are discussed, so as to fully understand biomechanical properties of intraluminal thrombi and aneurysmal tissues, as well as the influence of mechanical property changes on the AAA growth and remodeling under pathological environment. Then representative research findings on prediction of rupture risk by a series of experimental and computational biomechanical methods are reviewed, including finite element analysis on stress distributions on AAA wall, assessment of rupture risk index and judgment of rupture locations. The relevant microstructural changes caused by thrombus aging are described in detail, and the current situation of biomechanical studies on AAA and future challenges are briefly summarized.