Direct methods are commonly used by crystallographers to determine relatively small crystal structures.However, existing techniques do not appear to be extensible to larger structures. The recent development of a solution strategy called Shake-and-Bake, aimed at determining structures via local minimization and repeated Fourier transformations, allows for implicit constraints to be included. In this article, a description of the Shake-and-Bake algorithm is given, along with a detailed description of master/slave MIMD implementations on a network of Sun workstations, an Intel iPSC/860 Hypercube, and a Connection Machine CM-5. Our experimental results on known structures, including gramicidin A, are extremely encouraging. For example, based on efficient implementations of Shakeand-Bake on the iPSC/860 and CM-5, for known structures of 28, 84, and 127 nonhydrogen atoms, we obtain success rates of 19%, 1%, and 0.2%, as opposed to existing methods, which yield success rates of approximately 6%, 0.006%, and 0.0002%, respectively.