Subdivision surfaces are finding their way into many Computer Aided Design and Animation packages. Popular choices include Loop, Catmull-Clark, Doo-Sabin etc. Subdivision surfaces have many design advantages over traditional use of Non Uniform Rational B-Splines (NURBs). 3D mesh compression has become necessary for transferring and browsing 3D objects over the internet. MPEG-4 has included encoding capability for 3D polygonal meshes. Level of details (LOD), progressive transmission, and 3D streaming are possible applications of the mesh compression. Our paper looks at developing one such method for Loop surfaces. Our method can handle any arbitrarily topological non-boundary/boundary objects of any genus. The paper shows the process as well as some results, which are promising and therefore can be used as a lossy, compression scheme and a surface reconstruction method.