This study is focused on vibration analysis of a rectangular plate in partial coupled with a vertical bounded fluid. The fluid displacement potential satisfying the fluid boundary conditions is derived and the wet dynamic modal functions of the plate are expanded in terms of the finite Fourier series for a compatibility requirement along the contacting surface between the plate and the fluid. The natural frequencies of the plate coupled with sloshing fluid modes are calculated using Rayleigh–Ritz method based on minimizing the Rayleigh quotient. The proposed analytical method is verified by comparing the presented results with the results obtained by three–dimensional finite element analysis. Finally, the influence of hydrostatic pressure and fluid depth on the natural frequencies are examined and discussed in details.