Modeling organs for surgery simulation is a formidable challenge due to two reasons. First, the organs and body parts have not only very complex shapes, but are deformable too. The second challenge is to provide a mechanism for surgeons to interact with these complex anatomical objects. We present a novel multi-layer parameterized representation scheme that addresses the both challenges. In our approach, we use a 2D flat map representation for the 3D geometry of the organ, that can be used for rendering, collision detection, and deformation. The tool-organ interaction can be computed on the 2D flat maps and then mapped back to the 3D geometry of the organs. With this representation, we demonstrate that we can construct a practical and realistic environment for interactive surgery simulation.