The advancement of high-speed axial flow multistage compressors is impeded by a lack of detailed flow field information. Recent developments in compressor flow modeling and numerical simulation have the potential to provide needed information in a timely manner. This paper, which consists of two parts, will explore this topic. The first part will address the development of a computer program to solve the viscous form of the average-passage equation system for multistage turbomachinery. Programming issues such as in-core versus out-of-core data storage and CPU utilization (parallelization, vectorization, and chaining) will be addressed. Code performance will be evaluated through the simulation of the first four stages of a five stage, high-speed, axial flow compressor on a CRAY Y-MP8/8128 computer. The second part will address the flow physics which can be obtained from the numerical simulation. In particular, an examination of the endwall flow structure will be made, and its impact on blockage distribution assessed.