We present a multiple shape correspondence method based on dynamic programming, that computes consistent bijective maps between all shape pairs in a given collection of initially unmatched shapes. As a fundamental distinction from previous work, our method aims to explicitly minimize the overall distortion, i.e., the average isometric distortion of the resulting maps over all shape pairs. We cast the problem as optimal path finding on a graph structure where vertices are maps between shape extremities. We exploit as much context information as possible using a dynamic programming based algorithm to approximate the optimal solution. Our method generates coarse multiple correspondences between shape extremities, as well as denser correspondences as by-product. We assess the performance on various mesh sequences of (nearly) isometric shapes. Our experiments show that, for isometric shape collections with non-uniform triangulation and noise, our method can compute relatively dense correspondences reasonably fast and outperform state of the art in terms of accuracy.