Hemodynamic stresses are known to degenerate the arterial wall and be involved in the pathogenesis of intraeranial aneurysm formation and development. The present study simulates the formation and growth of aneurysms by focusing on the interplay between the wall shear stress, degeneration of the mechanical wall properties, and the wall deformation. We construct numerical aneurysm models arisen from both straight and curved arteries, and we hypothesize that high local wall shear stress larger than a certain threshold value will lead to a linear decrease in the mechanical property of the vessel wall. The degeneration of vessel wall leads to wall deformation and redistribution of the wall shear stress, which in turn leads to further degeneration of the wall. Development of aneurysm is observed in both the straight and curved models. In the straight model, the growth of aneurysm is small and mainly at the distal neck region, and the aneurysm stops growing after several steps. In contrast, in the curved model, the aneurysm continues to grow in height and width. Our computer simulation shows that even if the wall shear stress inside a saccular aneurysm is low, aneurysm development can occur due to degeneration of the wall distal and proximal to the aneurysm. The interaction between the geometry change and the wall degeneration is key to the development of aneurysms. The method demonstrates the potential utility of model-based numerical methods in the investigation of developmental biology of intracranial aneurysms.