In the human hand, the softness of a fingertip plays a significant role on stable grasping and dexterous manipulation. This paper presents a method of computing minimum grasp forces of a multi-fingered hand with soft fingertips. In the first, we built up a simple linear contact model of a soft fingertip. Then, based on Pontryagin's principle, the problem of minimizing contact forces for realizing the stable grasping was formulated and the forces were computed. Finally, the experiments were carried out using a multifingered robot hand, called "Allegro Hand" with hard fingertips and soft ones, and the effectiveness of the proposed method was validated.