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This paper deals with the problem of stable grasping in rolling manipulations with soft deformable fingertips in two-dimensional space and without the effect of gravity. Two rolling distance models for the soft-area contact motion and their effect on contact kinematics are considered. The modeling of contact forces in soft-area contacts is discussed and an analysis of a stable grasp is made. A simple feedback controller for stabilizing the grasp is proposed and tested in simulation. The control law is based on the object's equilibrium conditions and is designed so that it drives the system at rest by achieving a desired value for the normal contact forces and appropriate tangential forces to balance the moments created by the contact offset.