In the elds of virtual reality, physically-based simulation focuses on reproducing the motion and properties of real objects in virtual environments. Until now, various physically-based models of mechanical phenomena have been proposed in the literature, simulating several physical properties such as rigid, fluid or deformable behaviors of the multiple real-life objects. In this master thesis, we propose to simulate the torsion of any deformable object and its haptic rendering. We intend to create haptic and visual rendering of a virtual environment, in which objects can be twisted, either by the user or by the action of other objects of the environment. Our two contributions are first the introduction of a novel constraint for torsion modeling in a physically-based simulation, and second a novel coupling scheme for haptic rendering of 3D virtual object torsion.