Real-time simulation of knot-tying with visual and force feedback is essential to VR surgery training. We present a physics-based simulator that enables realistic knot tying at haptic speed. The virtual thread obeys Newton's laws and behaves naturally. The model covers mechanical properties of real thread such as stretching, compressing, bending and twisting, contact forces with self and the environment, and gravity. Its structure has essential advantages over geometrically based approaches.