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Contact and deformation modeling for interactive environments has seen many applications, from surgical simulation and training, to virtual prototyping, to teleoperation, etc., where both visual feedback and haptic feedback are needed in real-time (kHz). In this paper, we consider contacts between a rigid body and an elastic object and address a little studied problem: the modeling and rendering of compliant twisting or rotation of the rigid body on the surface of the elastic object and the associated effects in the deformation of the elastic object. We present a unique strategy to model the contact torques applied to the rigid body and the resulted shape deformation of the elastic object. This strategy extends the general paradigm of contact and deformable modeling introduced by the authors earlier  so that not only contact forces but also contact torques, not only compliant translations but also compliant rotations of the rigid body, as well as the resulted deformations of the elastic object can all be simulated in a combined update rate of over lfeHz. The strategy is implemented, and the experimental results confirm its effectiveness and efficiency.