A mathematical model for the rupture of cerebral saccular aneurysms is developed through the analysis of three-dimensional stress distribution in the aneurysm wall. We assume in this paper that a saccular aneurysm resembles a thin spherical shell (a spherical membrane), and then develop a strain-energy function valid for finite strain to analyze three-dimensional stress distribution in the aneurysm wall. We find that rupture occurs when the ratio of the wall thickness to the radius of the aneurysm is 6.1 × 10-3. We also conclude from our analysis that rupture can occur when the ratio of thickness to radius of the parent aneurysm equals the ratio of thickness to radius of the daughter aneurysm. These findings may be helpful to the neurosurgeon for predicting the rupture potential in patients presenting with unruptured aneurysms.