Vibration of orthotropic rectangular plates having viscoelastic point supports at the corners with symmetrically added four concentrated masses rigidly mounted on the two diagonals of the plate is analyzed. The Lagrange equations are used to examine the steady state response to a sinusoidally varying force applied at the centre of a viscoelastically point-supported orthotropic elastic plate of rectangular shape with the considered locations of the added masses. In the study, for applying the Lagrange equations, the trial function denoting the deflection of the plate is expressed in polynomial form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The influence of the locations of the added masses, mechanical properties characterizing the orthotropy of the plate material and the damping of the supports to the steady state response of the viscoelastically point-supported rectangular plates is investigated numerically for the concentrated load at the centre. Because of the symmetry of the supports and loading condition, only the first three symmetrical modes occur in the considered frequency range. Therefore, only the results of the first three symmetrical modes are given in the present study. Convergence studies are made. The validity of the obtained results is demonstrated by comparing them with other solutions based on the Kirchhoff-Love plate theory. (C) 2003 Elsevier Ltd. All rights reserved.