Massively parallel architectures have been proposed for large scale problems in associative processing, database management, artificial intelligence, image processing, etc. In a very large machine the cost of the PE interconnections is significant. The perfect shuffle and exchange connections are an attractive alternative to other connection schemes such as two-dimensional meshes, multi- stage networks and hypercubes. This project studies a massively parallel architecture where the processing elements are interconnected with perfect shuffle and exchange networks. Issues being investigated include how to best divide a machine into modules, how to add redundancy, how to control data routing, the architecture of each processing element and how to control each processing element.