A numerical method for the analysis of the free vibration behavior of thick skewed plates having arbitrary boundary conditions by using the Rayleigh-Ritz approach is presented in this paper, together with some numerical results. The method is based on the three-dimensional elasticity theory and skew coordinate system by considering rotating inertia and shear deformation. Numerical results are compared with the available ones in the literature. The comparison shows the method presented in this paper to be useful for analyzing the free vibration of thin and thick skewed plates having arbitrary boundary conditions. The effects of skew angles and aspect ratio of plates on the free vibratory characteristics of the thick skewed plates are also investigated.