We proposed a new hemodynamic indicator for the initiation of cerebral aneurysms, defined by the temporal fluctuations of tension/compression forces acting on endothelial cells. We calculated the proposed hemodynamic indicator and other three hemodynamic quantities (time-averaged wall shear stress (WSS), time-averaged spatial WSS gradient (SWSSG), and potential aneurysm formation indicator (AFI)) for a patient-specific geometry before aneurysm formation by means of computational fluid dynamics technique. The results showed that only the proposed hemodynamic indicator had a significant correlation with the location of aneurysm formation. Our findings suggest that the proposed indicator might be a prospective hemodynamic indicator for the initiation of cerebral aneurysms.