The use of liquid crystalline polymers (LCPs) as high strength materials has been limited almost exclusively to the formation of fibers such as Kevlar. This is because processing flows, other than fiber spinning, disrupt the long-range orientational order of these rather expensive materials. The mechanisms by which this occurs have remained elusive. In this study, we seek to explore this question in the context of theoretical models that have been proposed to describe LCPs. We consider the simplest of all possible flow geometries, namely the flow between parallel, flat boundaries, one of which is translating in its own plane. One reason for studying this flow is that there is a large body of experimental observations available for qualitative comparison. Although we are still at an early state of realizing our overall objectives, the work that I will discuss here seems to point in a positive direction for future studies.