This paper describes the modeling and simulation of fluid structure interactions (FSI) of involute-shaped fuel plates used in nuclear research reactors. We believe this to be the first time that this type of application is described in the literature using a fully-coupled, and monolithic, finite element approach. The simulations are validated against plate deflection data for the conceptual design of the Advanced Neutron Source Reactor (ANSR), which was envisioned to be the world's most powerful nuclear research reactor for neutron scattering and other applications, but was ultimately never completed. The involute-shaped fuel plates that were designed and tested for ANSR bounded the operating envelope, while still representative of the highly-enriched uranium (HEU) plates that are currently used, and future low-enriched uranium (LEU) plates that are proposed to be used in the High Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory (ORNL). As such, the findings from the present FSI analyses carried out herein for ANSR plates provide good guidelines and inform designers what should be expected for the next generation of plates. It is shown herein that the current approach can accurately capture the leading-edge deflections of the involute-shaped plates and simulations can predict the `S-shaped' deflection of the first mode instilling confidence in the methodology.