In one embodiment of the present invention, a position-based dynamics (PBD) framework provides realistic modeling and simulation for elastic rods. In particular, the twisting and bending physics of elastic rods is incorporated into the PBD framework. In operation, an elastic rod model generator represents the center line of an elastic rod as a polyline of points connected via edges. For each edge, the elastic rod model generator adds a ghost point to define the orientation of a material frame that encodes the twist of the edge. Subsequently, a PBD simulator solves for positions of both points and ghost points that, together, represent the evolving position and torsion of the elastic rod. Advantageously, the ghost points enable more realistic animation of deformable objects (e.g., curly hair) than conventional PBD frameworks. Further, unlike force based methods, elastic rod simulation in the PBD framework performs acceptably in environments where speed is critical.