Study of the development of aneurysm is a difficult task due to lack of experimental and clinical data. The current study takes advantage of fluid-structure interaction (FSI) to simulate the formation and growth of aneurysms by focusing on the interplay between the wall shear stress, degeneration of the vessel wall, and the wall deformation. We construct numerical aneurysm models arisen from both straight and curved arteries, under the hypothesis that high local wall shear stress larger than a certain threshold value will lead to a linear decrease in the wall mechanical properties. In the straight model, the growth of aneurysm is small and only 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 study shows that even if the wall shear stress inside an aneurysm is low, aneurysm development can occur due to degeneration of the wall distal and proximal to the aneurysm. Our study demonstrates the potential utility of rule-based numerical methods in the investigation of developmental biology of cardiovascular diseases.