Abstract: Cutting up a complex object into simpler sub-objects is a fundamental problem in various disciplines. In image processing, images are segmented while in computational geometry, solid polyhedra are decomposed. In recent years, in computer graphics, polygonal meshes are decomposed into sub-meshes. In this paper we propose a novel hierarchical mesh decomposition algorithm. Our algorithm computes a decomposition into the meaningful components of a given mesh, which generally refers to segmentation at regions of deep concavities. The algorithm also avoids over-segmentation and jaggy boundaries between the components. Finally, we demonstrate the utility of the algorithm in control-skeleton extraction.