This paper presents a hydroelastic vibration analysis of two identical rectangular plates obliquely coupled through a liquid medium. The proposed approximate model simulates components such as a part of pump impellers or divider plates in cylindrical liquid storage tanks. The wet dynamic displacements of the clamped rectangular plates are approximated using a combination of orthogonal polynomials or beam functions. To conserve liquid volume, the sectorial liquid column is transformed into an equivalent rectangular column. The liquid displacement potential function is derived satisfying both the Laplace equation and relevant liquid boundary conditions. The wet dynamic modal functions of the plates are expanded using finite Fourier-Bessel and Fourier series to ensure compatibility along the interface between the plates and the liquid. Natural frequencies of the liquid-coupled system are then computed via the Rayleigh-Ritz method. Validation against three-dimensional finite element analysis shows strong agreement with the analytical results. Finally, the influence of the oblique angle between the plates on the normalized natural frequencies is investigated.