In this article, the free vibration characteristics of a rectangular sandwich plate with a honeycomb core are investigated when the plate is positioned on the wall of a fluid-filled tank. The sandwich plate consists of two thin aluminum facesheets and an austenitic aluminum honeycomb core. To homogenize the honeycomb core, in addition to the classical Mlok–Gibson model, one of the latest available models, namely the Tournabene model, is employed to provide an innovative approach in this study. To model the dynamic behavior of the sandwich plate, three distinct analytical models are presented, and the advantages and limitations of each are discussed. The equations of motion are derived from Hamilton’s principle, and a layered analytical model is used to simulate the sandwich plate with Navier boundary conditions in contact with the fluid. In the fluid–structure interaction, the fluid is assumed to be ideal, incompressible, irrotational, and inviscid, and the coupling effect between the plate and the fluid in the transverse direction is considered, while shear effects are neglected. The analytical methods and homogenization relations are validated against prior research and three-dimensional finite-element simulations. Finally, the influence of parameters such as the dimention of the tank-to-plate length ratio, the fluid height from the bottom edge, the plate’s position on the wall, and the honeycomb-cell geometry on the submerged natural frequencies is analyzed and compared.