The skeleton is a low-dimension shape representation of 3D objects useful for different areas, such as machine vision, image processing, computer graphics, character animation, and etc. The most common techniques for skeleton computing are based on the Reeb graph and the shortest path finding. Using only the shortest path algorithms for extracting the critical points and constructing the Reeb graph over the surface of the model may generate unwanted skeleton joints. A new skeleton pruning method for removing the spurious skeleton joints is introduced that is based on the medial axis transform and the geodesic distance function. Consequently, the generated skeleton can capture in a simple and meaningful way the essential shape of the 3D objects in a compact form.