In current clinical practice, aneurysm diameter is one of the primary criteria used to decide when to treat a patient with an abdominal aortic aneurysm (AAA). It has been shown that simple association of aneurysm diameter with the probability of rupture is not sufficient, and other parameters may also play a role in causing or predisposing to AAA rupture. Peak wall stress (PWS), intraluminal thrombus (ILT), and AAA wall mechanics are the factors most implicated with rupture risk and have been studied by computational risk evaluation techniques. The objective of this review is to examine these factors that have been found to influence AAA rupture. The prediction rate of rupture among computational models depends on the level of model complexity and the predictive value of the biomechanical parameters used to assess risk, such as PWS, distribution of ILT, wall strength, and the site of rupture. There is a need for simpler geometric analogues, including geometric parameters (e.g., lumen tortuosity and neck length and angulation) that correlate well with PWS, conjugated with clinical risk factors for constructing rupture risk predictive models. Such models should be supported by novel imaging techniques to provide the required patient-specific data and validated through large, prospective clinical trials.