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The Investigation presents the formulation of a general equation of motion and its analytic and numerical solution for the determination of the dynamic deflections and stresses of a multilayered rectangular plate on viscoelastic foundation subject to a constant force travelling at a constant velocity. Various combinations of simply-supported, clamped, and free edge conditions of the plate are studied. A multi-layered plate has in general two shifting "neutral" planes, one in which ax«=0 while OyfQ and another, 0y“O while Oj^O. They are not only at different locations, but also change their locations in the plate depending on the loads or curvatures of bending. The two "neutral" planes become one and fixed in the plate, i.e., ax=*Oy=0 only when (a) the Poisson's ratios of all the layers are the same, (b) bending moments are the same about x and y axis and (c) the layers are symmetrically arranged. The equation of motion is solved by expressing the deflection function of the plate and the moving load in the form of a double series of normal mode functions of two orthogonal plate strips, diagonalizing the stiffness matrix and making use of the Laplace transformation method. The validity of general formulas developed is verified by reducing them into special cases for comparative studies with the published works. To Illustrate the general methodology developed, three plates having SSSS, SSFF, and CCCC edge supports are studied. Computer programs newly developed, together with those commercially available subroutines are used, and the effects of some parameters are illustrated and briefly discussed.