The superiority of deformable human fingertips as compared to hard robot gripper fingers for grasping and manipulation has led to a number of investigations with robot hands employing elastomers or materials such as fluids or powders beneath a membrane at the fingertips. In this paper, to analyze the stability of dynamic control of an object grasped between two soft fingertips through a soft interface using the viscoelastic material between the manipulating fingers and a manipulated object is modeled through bond graph method (BGM). The fingers are made viscoelastic by using springs and dampers. Detailed bond graph modeling (BGM) of the contact phenomenon with two soft-finger contacts considered to be placed against each other on the opposite sides of the grasped object as is generally the case in a manufacturing environment is presented. The stiffness of the springs is exploited in order to achieve the stability in the softgrasping which includes friction between the soft finger contact surfaces and the object, The paper also analyses stability of dynamic control through a soft interface between a manipulating finger and a manipulated object. It is shown in the paper that the system stability depends on the viscoelastic material properties of the soft interface. Method of root locus is used to analyze this phenomenon. The paper shows how the weight of the object coming downward is controlled by the friction between the fingers and the object during the application of contact forces by varying the damping and the stiffness in the soft finger.