This paper develops the kinematic, dynamic and contact models of a three-fingered robotic hand (BarrettHand) in order to obtain a complete description of the system which is required for manipulation tasks. These models do not only take into account the mechanical coupling and the breakaway mechanism of the under-actuated robotic hand but they also obtain the force transmission from the hand to objects, which are represented as triangle meshes. The developed models have been implemented on a software simulator based on the Easy Java Simulations platform. Several experiments have been performed in order to verify the accuracy of the proposed models with regard to the real physic system.