Fluid compressibility of liquids is often neglected in engineering design. However, the error incurred due to this simplification is not well identified. This paper examines the influence of compressibility on the hydroelastic vibration of plates in contact with fluid. An analytical solution for the free vibration of thick rectangular isotropic plates coupled with a bounded compressible inviscid fluid domain is developed. Plate displacement theories with arbitrary order are considered using the 2D Carrera Unified Formulation, which can obtain results very similar to 3D solutions. The eigenvalue problem is obtained by considering the kinetic and potential energy of both the fluid and the plate. The displacement variables are evaluated using the Ritz method. A comparison of the results with open literature and 3D finite element software is performed. Parametric studies are carried out in order to assess the error due to neglecting fluid compressibility as a function of plate geometry, material properties and boundary conditions. The influence of fluid domain size, density and sonic velocity is also assessed. The results indicate that the error due to neglecting fluid compressibility is high when thick, square plates made of light, stiff materials and with rigid boundary conditions are considered.