The free vibration analysis of symmetrically laminated thick rectangular plates is examined. Thep-Ritz method is employed in which sets of uniquely defined polynomials are used as the admissible trial displacement and rotation functions. The energy integral expressions of the laminates are derived by incorporating the shear deformation using Reddy’s higher-order plate theory [J. Appl. Mech. ASME51, 745–752 (1984)]. The formulation is basically applicable to rectangular laminates with any combination of free, simply supported, and clamped boundary conditions. To evaluate the validity and to demonstrate the applicability of the proposed method, a series of free vibration analyses of laminated composite plates is reported. Wherever possible, the accuracy of this analysis is validated through comparison with available results. Efforts are made to interpret the results to provide physical insight to the problem.