According to the most recent statistics, cerebrovascular disease is the third leading cause of death in the United States, ranking behind heart attack and all forms of cancer. One form of cerebrovascular disease is the cerebral aneuiysm, which manifests itself as a dilatation, or pouching, of the arterial wall. The dilatation develops at a diseased site along the wall into a distended sac of stressed arterial tissue. Fully developed cerebral aneurysms are typically from 5 to 10 millimeters in diameter. Aneurysms can and do occur at any point within the cardiac and peripheral vasculaturc. However, cerebral aneurysms tend to assume a simple spherical form that makes them well suited to a biophysical analysis. They also pose the greatest risks to the patient. Left untreated, an aneurysm continues to expand until it raptures, causing hemorrhage, severe neurological complications and possibly death. It is for these reasons that this article concentrates on cerebral aneurysms. Many aspects of the treatment given here will be applicable to other types of aneurysms.