An aneurysm's rupture is commonly associated with its maximum diameter, yet biomechanical studies emphasize the significant influence of mechanical wall shear stress (WSS) in this process. This study focuses on two models of aortic aneurysms: abdominal aortic aneurysm and descending thoracic aortic aneurysm. Five cases, comprising two for model 1 and three for model 2, are examined to explore both axisymmetric and asymmetric shapes, as patient geometry may manifest as either fusiform (axisymmetric) or saccular (asymmetric), while maintaining a consistent aneurysm diameter and adjusting the bulge shape factor to induce asymmetry. Hemodynamic factors, including WSS and wall shear stress gradient, are computed to evaluate thrombus formation and rupture risk within the aneurysms. Our results indicate the presence of recirculation zones in both the medial and transverse planes, generating vortices within the aneurysm. These vortices are more prominent in asymmetric cases compared to axisymmetric cases, leading to increased blood residence time within the aneurysm and a higher likelihood of thrombus formation. Thrombus formation can further impede blood flow, heightening the risk of embolism or ischemic events. Rupture occurs when the WSS surpasses tissue strength; thus, if the tissue strength of all aneurysms is same, our findings suggest that rupture risk varies according to asymmetry. In the transverse direction, our results demonstrate that in model 1, case 1 exhibits uniform WSS on both sides, while in case 2, WSS is higher at the posterior sides of the aneurysm sac. Conversely, in model 2, WSS is higher at the anterior side of the aneurysm. In the medial direction of the aneurysm, WSS is highest for case 5, followed by case 3, case 4, case 2, and case 1, respectively, indicating elevated WSS when the anterior bulge dominates over the posterior bulge for each model. Overall, a higher rupture risk is observed in model 2 compared to model 1 due to increased mechanical stresses.