This paper discusses the grasp stability under gravity where each finger makes soft-finger contact with an object. By using the intersection of polygon models between a finger and an object, the contact area between a finger and an object is obtained. Then, by assuming the Winkler elastic foundation model, the pressure distribution within the contact area is obtained. By using this pressure distribution, we determine the grasp stability under soft-finger contact. We further consider defining a quality measure of the soft-finger grasp by assuming that, while the gravitational force is applied to an object, the direction of gravity is unknown. To demonstrate the effectiveness of the proposed approach, we show several numerical examples. Finally, we show an experimental results on identification of physical parameters of elastic material attached at the finger surface.