The genesis and development of intracranial aneurysm have long been of interest but remain not understood. In the present study we simulate the progression of intracranial aneurysms by constructing a computational model of a curved artery. It is hypothesized that high local wall shear stress above a threshold value will lead to degeneration of the arterial wall mechanical properties. And this degenerative effect may continue even after the wall shear stress has become lower than the threshold, which is referred to as the "time remaining effect" in this study. We performed several groups of studies using both assumptions and aneurysm development is observed as result of the interplay between high wall shear stress, wall degeneration and wall deformation. In the growth of aneurysms with "time-remaining effect", the increase of aneurysmal height accelerates in later steps. It is concluded that computer simulation can yield insight into the understanding of the pathophysiology of aneurysmal initiation and growth, and help in clarifying the role of certain hemodynamic parameters.