- In this paper, we adopt the first-order shear deformation theory in the moving least squares differential quadrature (MLSDQ) procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates. The transverse deflection and two rotations of the laminate are independently approximated with the moving least squares (MLS) approximation. The weighting coefficients used in the MLSDQ approximation are obtained through the fast computation of the MLS shape functions and their partial derivatives. The natural frequencies of vibration are computed for various laminated plates and compared with the available published results. Through numerical experiments, the capability and efficiency of the MLSDQ method for eigenvalue problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined. Effects of the size of support, order of completeness of the basis functions and node irregularity on the numerical accuracy are also investigated. 2003 Elsevier Science B.V. All rights reserved.