Hemodynamics is believed to play a vital role in the initiation of cerebral aneurysms. In this study, we describe a newly defined hemodynamic quantity, the gradient oscillatory number (GON), as an index for the cerebral aneurysm initiation. It is defined by temporal variations of flow-induced tension/compression forces acting on endothelial cells. We calculated the index for the arterial geometry before aneurysm formation, which was constructed by artificially removing the aneurysm from a medical image-based arterial geometry. The result showed that the index had a strong correlation with the location of aneurysm formation. This suggests that the proposed index, GON, may be useful as a hemodynamic index for the initiation of cerebral aneurysms.