Soft fingers contribute to dexterous grasping on account of the area contact and high friction involved. This paper presents a novel approach in modeling of soft contacts between soft fingertip and object using viscoelastic material and analyses its characteristics employing BondGraph Methods (BGM). The fingers are made viscoelastic by using springs and dampers. Detailed bond graph modeling 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 soft-grasping which includes friction between the soft finger contact surfaces and the 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 moving 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.