This paper presents a grasp planner which allows a robot to grasp the constricted parts of objects in our daily life. Even though constricted parts can be grasped more firmly than convex parts, previous planners have not sufficiently focused on grasping this part. We develop techniques for quadric surface approximation, grasp posture generation, and stability evaluation for grasping constricted parts. By modeling an object into multiple quadric surfaces, the planner generates a grasping posture by selecting one-sheet hyperbolic surfaces or two adjacent ellipsoids as constricted parts. When a grasping posture being generated, the grasp stability is evaluated based on the distribution of the stress applied to an object by the fingers. We perform several simulations and experiments to verify the effectiveness of our proposed method.