Bending problems of functionally graded rectangular plates were analyzed. In terms of Plevako function, assuming that the Yang's modulus of the material was distributed through a power function in the thickness direction, an exact solution of bending problem of simply supported functionally graded rectangular plates was obtained by variable separation method. Through numerical examples, the variations of displacement and stress components with different graded material distributions were analyzed and different graded parameters were found to have significant effects on the structural behavior. The research serves as theoretical basis for the development of numerical methods and simplified theories of functionally graded material structure.