The Markov-Modulated Bernoulli Process (MMBP) model is used to analyze the delay experienced by messages in clocked, packed-switched Banyan networks with k X k output-buffered switches. This approach allows us to analyze both single packet messages and multipacket messages with general traffic pattern including uniform traffic, hot-spot traffic, locality of reference, etc. The ability to analyze multipacket messages is very important for multimedia applications. Previous work, which is only applicable to restricted message and traffic patterns, resorts to either heuristic correction factors to artificially tune the model or tedious computational efforts. In contrast, the proposed model, which is applicable to much more general message and traffic patterns, not only is an application of a theoretically complete model but also requires a minimal amount of computational effort. In all cases, the analytical results are compared with results obtained by simulation and are shown to be very accurate.