Delta networks are multistage interconnection networks that can be used to communicate rapidly between components of a modular system. In this thesis their performance is examined and evaluated for two types of message passing: circuit switching and packet switching. In circuit switching, a start packet enters the network as the first packet in the message and reserves a path for the rest of the packets. At the end of the message, an end packet cleans up the path by releasing the switches in the path set by the start packet. In packet switching there is no start packet to reserve the path and so each packet of the message contends on its own for every switch in its path. The performance of circuit switching is found to be as good as or better than that of packet switching in terms of throughput and message delay, with packet switching being better for initial delay. The effects of changes in network parameters is also examined for both schemes and the differences are discussed. Network parameters that are varied are the time taken to pass a packet through a switch, the time taken to decode the address for the next switch, the size of the buffers between the stages, the size of the network, and the length of the messages.