Towards the establishment of the preventive medical care for the cerebral aneurysm, this paper proposes an SVM based method for building a discrimination function that classifies the presence or absence of the cerebral aneurysm using the cerebral blood vessel's shape features obtained from medical images such as MR images. Using the discrimination function, this paper explores how much each feature affects the onset of the cerebral aneurysm. This paper deals with the internal carotid artery (ICA). The blood vessel (ICA)'s shape features are extracted from medical images of 18 persons without cerebral aneurysm and 13 patients with a cerebral aneurysm. From the medical image, the cross sections and centerline of the ICA are obtained. The cross sections are divided into nine sections along the centerline. Shape features such as the cross sectional area, its circularity, curvature, torsion, length of the centerline and branch angles are obtained in each section; as a total, 113 features including the mean and variance of some features in each section are used for building the SVM. As a result of conducting the experiments, the accuracy for discriminating the presence/absence of the aneurysm by the SVM is 90.3%. In the obtained discrimination function, the coefficient values of the function can be considered how much the features affect the onset of the aneurysm. The features that could significantly cause the onset of the cerebral aneurysm are clarified, and the reasons why these features are significant are discussed.