The subjects described in this paper are a real-time adaptive modeling method for deformable objects and an adaptive cutting method for 3D surface meshes. In the literature so far, adaptive models with high resolution representations at regions of high deformation have not been investigated. In this paper we propose a new method for real-time modeling of soft objects, of which high resolutions dynamically adapt to the regions of high deformation. In order to reduce the computational cost in comparison with the previous methods we use the bisection refinement algorithm. The experimental results show the effectiveness of the proposed method. The cutting operation of 3D surface meshes plays an important role in surgery simulators. One of the important requirements for surgical simulators is the visual reality. We propose a new strategy for cutting on surface mesh: refinement and separate strategy consisting of the refinement followed by the separation of the refined mesh element. Since the advantage of the low computational cost, the bisection refinement method is utilized for the refinement process. The proposed strategy gives the faithful representation of the interaction path.