The present works are the theoretical results of the study to develope a damping flexible coupling which has a high performance of control for the torsional vibrations of power shafts in a large machinery. It is established the analysis scheme of the multiple-leaf spring, to obtain the static coefficient of stiffness of the coupling. Also, the dynamic coefficient of stiffness and the damping coefficient of the coupling are indentified through the flow analysis for a induced flow of working fluid by the deflection of multiple-leaf springs. This paper dealt with damping contributions by the friction between each plate of the multiple-leaf spring. In this paper, it is found that the dynamic characteristics of the damping flexible coupling are strongly dependent on the stiffness and the number of the multiple-leaf spring, and also vary with the viscosity of working fluid and the vibration speed of the inner star.