Low velocity impact behavior of rectangular plates made of functionally graded materials (FGMs) based on three-dimensional theory of elasticity is studied in this paper. The modified Hertz contact law, which is appropriate for graded materials, is employed. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the graded finite element modeling is applied. Solution of the nonlinear resulted system of equations in the time domain is accomplished via an iterative numerical procedure based each time on Newmark's integration method. The effects of various involved parameters, such as the graded property profile, projectile velocity and projectile density on time histories of contact force, lateral deflection and normal stresses are investigated in detail. To present efficiency of the present work, several numerical examples are included. The main novelty of the present research, which has not been reported in literature, is considering the difference of lateral deflection through the thickness of the FGM plate due to analyzing three-dimensional elasticity of the plate.