Abstract: Proposed is a quasi-3D shear deformation plate theory that can be used for bending and free vibration analysis of functionally graded material (FGM) plates. The novelty of the theory is that it contains only four variables and takes into account the effect of thickness stretching. Based on this theory, the governing equations for the bending and free vibration problems of a functionally graded rectangular plate are derived using Hamilton's principle, and the analytical solutions of the bending displacements, stresses, and the fundamental frequencies of free vibration are obtained by using the Navier method. Comparing with the 3D theory, other quasi-3D plate theories containing more variables, and two-dimensional plate theories verifies the accuracy of the theory. Numerical results show that the theory proposed can effectively and accurately predict the bending and free vibration behaviors of FGM plates, and can significantly reduce the amount of computation.