The flexural vibration characteristics of rectangular plates with linearly varying thickness is examined. The fourth order differential equation is solved by using Lagrange multiplier method. The thickness of the plate varies linearly along x axis and this variation is taken to be symmetric with respect to the middle surface. Simplicity and quick convergence is the advantage of the method in comparison with other much more laborious numerical metods which require extensive computer facilities A power series is used as an admissible function for the displacement function