In this paper we present a new framework, based on subdivision surface approximation, for efficient compression and coding of 3D models represented by polygonal meshes. Our algorithm fits the input 3D model with a piecewise smooth subdivision surface represented by a coarse control polyhedron, near optimal in terms of control points number and connectivity. Our algorithm, which remains independent of the connectivity of the input mesh, is particularly suited for meshes issued from mechanical or CAD parts. The found subdivision control polyhedron is much more compact than the original mesh and visually represents the same shape after several subdivision steps, without artifacts or cracks, like traditional lossy compression schemes. This control polyhedron is then encoded specifically to give the final compressed stream. Experiments conducted on several CAD models have proven the coherency and the efficiency of our algorithm, compared with existing methods.