Abstract: Haptics on 3D deformable models is a challenge because of the inevitable and expensive 3D deformation computation. In this paper, we propose a new technique that extends the conventional rigid geometry images approach proposed by Gu et al. [9]. Our approach not only flattens the geometry, but also helps to accomplish deformation in an effective and efficient manner. Our approach is suitable for haptics computing, as it performs the deformation on the geometry map itself thereby avoiding the expensive 3D deformation computation. We demonstrate construction of the deformable geometry map representation and its application utilizing practical methods for interactive surgery simulation and interactive textile simulation.