Fluid-structure interaction in hypersonic flow has seen an increased interest among researchers in response to the worldwide race to sustainable hypersonic flight. The interaction between inertial, elastic, aerodynamic, and thermal loads in high Mach flows is an extension of classical aeroelasticity. To investigate the fundamental physics that govern the aero-thermal-elastic interaction, elastic plates are utilized in super/hypersonic wind tunnel experiments for their relative simplicity of installation, manufacture, and analysis. Numerous recent experiments investigated the response of elastic plates using advanced measurement techniques (for pressure, temperature, and deformation) focusing on shock-wave/boundary-layer and structure interaction, flutter onset and limit-cycle oscillation, and impinging shock effects, with more planned for the upcoming years. Many of those experimental studies are published with little, and in some cases no, computational or theoretical fluid-structure analysis. This demonstrates the need for accurate and accessible theoretical models for the analysis of plates in hypersonic flow with the different physical effects included. In the present work, theoretical-computational models of plates in hypersonic flow are derived and formulated to be used in linear and nonlinear analysis of static and dynamic problems. An overview of the derivation of a plate-cavity-freestream model is presented. A novel structural model is derived that includes the effect of elastic in-plane edge constraints, which is shown to be important to the nonlinear static and dynamic plate response. Analysis of recent experiments conducted by researchers from the US Air Force Research Laboratory and the University of Maryland is presented with correlation between theory and experiment.