We address the problem of correspondence between 3D isometric shapes. We present an automatic method that finds the optimal correspondence between two given (nearly) isometric shapes by minimizing the amount of deviation from isometry. We optimize the isometry error in two steps. In the first step, the 3D points uniformly sampled from the shape surfaces are transformed into spectral domain based on geodesic affinity, where the isometry errors are minimized in polynomial time by complete bipartite graph matching. The second step of optimization, which is well-initialized by the resulting correspondence of the first step, explicitly minimizes the isometry cost via an iterative greedy algorithm in the original 3D Euclidean space. Our method is put to test using (nearly) isometric pairs of shapes and its performance is measured via ground-truth correspondence information when available. ©2010 IEEE.