In this work, we present an effective anatomy preserving model decomposition technique. By extracting unit-width curve skeletons, which are robust to noise, and mapping skeleton branches to model surface nodes, our method accurately identifies the topology and geometry information of a 3D model, resulting in more semantically rich segmented components. Experiments on 2194 models from the Princeton Shape Benchmark and A Benchmark for 3D Mesh Segmentation demonstrate the advantage of the proposed technique. Our results preserve better anatomical structures compared to three commonly used model segmentation methods.