This research will utilize numerical simulation to address the influence of end-walls on the flow in the space between eccentric rotating cylinders. The common belief that such effects disappear when the end-walls are sufficiently far apart is called into question by results developed through earlier results by these researchers, who focus on the development of instabilities in this flow. The present study will generalize and systematize the role of end-walls in structuring the possible instability modes which may occur. The configuration to be studied is representative of flows in certain types of bearings and other tribological systems, where instabilities may cause unanticipated dynamics and loss of efficiency.