Haptic modeling of organs using existing approaches is still not realistic or real time. We propose and develop the mathematical foundation of a new approach to modeling organs using beams. Beams are well known entities in Civil and Structural engineering. We develop their mathematical properties in the context of organ simulation. The real time advantage arises from the fact that a single beam implementation eliminates hundreds, if not thousands of mass springs from the traditional mass spring models and, thousands of polygons from the finite element method. Even more importantly, our derivation is valid for large deformation. Most previous work has developed equations only for small deflections. Large deformation is important because we set out to simulate blunt cutting which requires models for large deflections. Our new model, when simulated and compared with an FEM model provides comparable accuracy.