Cerebral aneurysms are local expansions of blood vessel walls in the brain blood system. The rupture of an aneurysm is a very severe event associated with a high rate of mortality. When cerebral aneurysms are detected, clinicians need to decide if operation is required. The risk of aneurysm rupture is then compared to the risks associated with the medical intervention. In the present paper, a probabilistic framework for a mechanically based rupture risk assessment of cerebral aneurysms is proposed. The method is based on the assumption that the strength of aneurysmal tissues can be described by a statistical distribution. A structural analysis of the aneurysm in question is performed, and the maximum stress experienced by the aneurysm is compared to the strength distribution. The proposed model was compared with clinical results for ruptured aneurysms in terms of rupture density and accumulated rupture risk as a function of aneurysm size. The model was able to reproduce the clinical results well. The proposed framework may potentially be used under in vivo conditions to predict the risk of rupture for diagnosed aneurysms.