The vibration of generally orthotropic rectangular elastic plates having viscoelastic point supports at the corners is analyzed. Lagrange's equations are used to examine the free vibration characteristics and steady state response to a sinusoidally varying moment affecting the center of a viscoelastically point-supported, generally orthotropic elastic plate of rectangular shape. For applying the Lagrange's equations, the trial function denoting the deflection of the plate is expressed in polynomial form. By using the Lagrange's equations, the problem is reduced to the solution of a system of algebraic equations. The influence of the off-axis angle, of the mechanical properties, and of the damping of the supports to the steady state response of the viscoelastically point-supported rectangular plates is investigated numerically for a concentrated moment at the center for various values of the mechanical properties characterizing the anisotropy of the plate material, for various off-axis angles and for various damping of supports for a given stiffness of supports. The results are given for the considered frequency range of the external periodical moment. Convergence studies are performed. The validity of the results obtained is demonstrated by comparing them with the solutions of specially orthotropic plates based on the Kirchhoff-Love plate theory. © TÜBİTAK.