We approximate the loop motions of various proteins by using a coarse-grained model and the theory of rubberlike elasticity of polymer chains. The loops are considered as chains where only the first and the last residues thereof are tethered by their connections to the main structure; while within the loop, the loop residues are connected only to their sequence neighbors. We applied these approximate models to five proteins. Our approximation shows that the loop motions can usually be computed locally which shows these motions are robust and not random. But most interestingly, the new method presented here can be used to compute the likely motions of loops that are missing in the structures.