Abstract: Deflection of rectangular plates of variable thickness resting on an elastic foundation is studied. The fourth order differential equation is solved by using the Garlerkin method. The thickness of plate is assumed to vary linearly along the x axis and this variation is taken to be symmetric with respect to the middle surface. The center deflection has been computed for different values of the taper parameter, aspect ratios and foundation modulus. Simplicity and quick convergence are the advantages of the present method in comparison with more laborious numerical methods requiring extensive computer facilities.