Parallel-flow induced vibrations of both large and small reactor internal structures have been analyzed in the past for multiple reactor types. In parallel flows relating to annular and leakage flows, the possibility for significant wear issues can arise and need to be assessed as has been shown throughout the literature. With parallel flow induced vibration, a particular fluid-structure interaction known as hydroelastic instability can arise. If hydroelastic instability occurs, damage to components can be severe and/or catastrophic. This particular phenomenon has been studied in the literature and a few empirically derived methodologies have been published to evaluate the potential for hydroelastic instability to occur in both a limited number of specific geometries and some generic geometries. However, as structural components and their associated flow field characteristics can vary significantly and because of the potential for catastrophic damage to reactor components and the associated costs, a more detailed first principles approach may be warranted to further determine if hydroelastic instability is not only possible, but probable. A potential design for a reactor internals test in which part of the upper internals would exhibit significant annular parallel flow velocities is analyzed for the potential onset of hydroelastic instability. In particular, the upper core plate, which is attached to the rest of the upper internals via support columns in a pendulum setup with the attachment/pivot point at the upper pressure vessel head flange, is temporarily designed to carry a significant non-prototypic pressure drop causing significant upper core plate to core barrel gap flow velocities and potential instability issues. Due to the different geometry of this hardware configuration compared to those found in the literature, both an empirically-based stability analysis from the literature and a first-principles based hydroelastic stability analysis are conducted. The first-principles analysis derives and solves the time-dependent equations of motion and mass conservation for both the fluid and structure and compares the results proximity to stability limits found in the literature. A comparison of the empirically based stability assessment with the first-principles stability analysis is made. Furthermore, an assessment of the probability for the onset of hydroelastic instability of the upper internals assembly is made via a Monte Carlo simulation using the first-principles analysis methodology.