Vibration of orthotropic rectangular plates having viscoelastic point supports at the corners under the effect of sinusoidally varying concentrated moment is analyzed. The Lagrange equation is used to examine the free vibration characteristics and the steady state response to a sinusoidally varying concentrated moment acting at the centre of a viscoelastically point-supported orthotropic elastic plate of rectangular shape. In the study, for applying the Lagrange equation, the trial function denoting the deflection of the plate is expressed in the polynomial form. By using the Lagrange equation, the problem is reduced to the solution of a system of algebraic equations. The influence of the mechanical properties, and of the damping of the supports on the mode shapes and the steady state response of the viscoelastically point-supported rectangular plates is investigated numerically, for a concentrated moment at the centre for various values of the mechanical properties which characterize the anisotropy of the plate material and for various damping ratios. The results of the natural frequencies are given for the first three antisymmetrical-symmetrical modes, and the steady state responses to a sinusoidally varying concentrated moment are determined for the frequency ranges of the first two antisymmetrical-symmetrical mode types. Convergence studies are made. The validity of the obtained results is demonstrated by comparing them with other solutions for free vibration analysis of point-supported or completely free rectangular plates for the first three antisymmetrical-symmetrical vibration modes based on the Kirchhoff-Love plate theory. (C) 2003 Elsevier Ltd. All rights reserved.