This study is investigated the forced vibration analysis of a moderately thick rectangular plate under moving load, which are composed of functionally graded materials and floating on incompressible fluid. The governing equations of the plate are analytically derived based on First-order Shear Deformation Theory (FSDT) with consideration of rotational inertial effects and transverse shear stresses. In order to obtaining the applied pressure on the free surface plate, the method of added mass is used. At first, the natural frequencies and shape modes of the rectangular plate with two parallel simply-supported edges are determined by decoupling and solving the motion equations system. Then, the forced vibration of the plate is investigated by shape mode expansions. Finally, the results of this study are compared and validated with results of other works and the effects of the different geometrical parameters such as the length to width ratio, the height to length ratio, fluid density, fluid depth and index of volume fraction on the dynamic response of the plate are investigated.