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Grasping of an object by robot hand is always challenging due to the uncertainties such as robot nonlinearities, unstructured objects with unknown location and stiffness, unknown contact types. To address these challenges, the fundamental task is to achieve the mathematical model of the robot hand, collect information about the object and model the contact between the hand and the object. In this paper, mathematical model of a three fingered Barrett Hand is developed using the Lagrangian method. Joint and cartesian space motions are simulated on the basis of computed torque algorithm. A contact model is then developed for hand-object coupled system assuming that the object properties are well known. Contact model is also simulated under different environment stiffness. Simulation studies verify the joint and cartesian space motions along with the estimated contact force. Implementation of the control for optimizing the contact force will be presented soon.