Using the soft fingers increases stability and dexterity in object grasping and manipulation. This is because of the enlarged contact interface between soft fingers and object. Although slippage phenomenon has a crucial role in robust grasping and stable manipulation, in the most of previous researches in the field of finger manipulation, it is assumed that the slippage between finger and object does not occur. In this paper, slippage dynamic modeling in object grasping and manipulation using soft fingers is studied. Because of the enlarged contact interface between soft fingers and object, a frictional moment along with tangential frictional force and normal force is applied on the contact interface. Therefore, a novel method for dynamic modeling of planar slippage using the concept of Friction Limit Surface is presented. In this method, equality and inequality relations of different states of planar contact is rewritten in the form of a single second-order differential equation with variable coefficients. These coefficients are determined based on the slippage conditions. This kind of dynamic modeling of contact forces can be used for designing the controllers to cancel the undesired slippage. The method is used in study of slippage analysis of a three-link soft finger manipulating a rigid object on a horizontal surface. In order to increase the accuracy of dynamic modeling of soft finger, dynamics of soft tip is integrated with the dynamic of finger linkage. Dynamic behavior of this system is shown in the numerical simulations.