In this paper we present a method for flexible protein structure alignment based on elastic shape analysis of backbones, in a manner that can incorporate different characteristics of the backbones. In particular, it can include the backbone geometry, the secondary structures, and the amino-acid sequences in the matching process. As a result, a formal distance can be calculated and geodesic paths, showing optimal deformations between conformations/structures, can be computed for any two backbone structures. It can also be used to average shapes of conformations associated with similar proteins. Using proteins from SCOP and PDB databases we demonstrate the matching and clustering of proteins using the backbone geometries, the secondary labels and the primary sequences. We demonstrate almost 92% success rate in automatic clustering of 100 proteins from SCOP database.