A single instruction stream-multiple data stream (SIMD) machine must have an interconnection network to pass data between processing elements. A model of SIMD machines is introduced which allows a formal mathematical analysis and comparison of different interconnection networks. Five interconnection networks that have been proposed in the literature are defined in terms of the model. They include a network similar to the one used in the STARAN, a network similar to the one recommended by T. Feng to implement data manipulating functions, the Illiac IV network, and the Perfect Shuffle. The networks are evaluated in terms of the upper and lower bounds on the time required for each network to simulate the actions of the others.