The individual risk of rupture of cerebral aneurysm is major concern in the clinical care of the asymptomatic aneurysms. The aneurismal rupture occurs when the intra-parietal stress exceeds the rupture stress of the material constituting the wall. The goal of our study is to give a new biomechanical measure of the individual risk of rupture of cerebral aneurysms. In a first phase, an experimental study was lead to characterize the biomechanical behavior of the aneurismal wall on 16 samples of aneurysm removed surgically. The testing on the samples of aneurismal sacs allows us to reach three main categories for each sex (male and female): soft, intermediate and stiff. All the unruptured aneurysms belong to the stiff or intermediate category whereas all the ruptured aneurysm corresponds to the soft category. That allows us to highlight a correlation between the risk of rupture and the material properties of the aneurismal wall. In a second phase, fluid/structure interaction computations (FSI) were performed to compare the deformations of a "patient-specific" aneurysm composed of a degraded and undegraded material. The results show that the material properties have a major impact on the scale of the aneurismal volume variation over the cardiac cycle. The volume variation differences according to the characteristics of the material are potentially viewable with the medical imaging. A parametric study of the input parameters was presented and showed the robustness of the results. Then, we demonstrated on 12 patient specific cases of different aneurysms (shape, size, location,...) that a significant difference of the volume variation over the cardiac cycle still exist between an aneurismal wall composed of a soft and a stiff material. This study suggests that the volume variation could be used as a base for an evaluation of the individual risk of rupture of cerebral aneurysms.