In this study, a simply and efficient closed form solution for bending and stress analysis of functionally graded circular and annular plates with elastic boundary conditions is presented based on the first order shear deformation theory (FSDT). By using the presented solution procedure, functionally graded plates subjected to arbitrary non-uniformly distributed normal and shear loads may be analuzed and all of stresses components may be exactly achieved. Shear loads may be imposed on the top and bottom surfaces of plate. By using the constitutive equations based on the first-order shear deformation theory, the transverse shear stress components cannot be obtained correctly and constant through-the-thickness distributions will be extracted. So, to achieve the transverse normal and shear stresses components in the proposed solution procedure, the three dimensional theory of elasticity is applied. To establish the accuracy and efficiency of the proposed approach, the obtained results are compared with other available published results and results of the three-dimensional theory of elasticity extracted from the ABAQUS software based on the finite element method (as the most exact method). Comparisons show that the obtained results are very accurate, while it is computationally quite more economic than the three-dimensional elasticity approach. Also, transverse normal and shear stresses boundary conditions on the top and bottom surfaces of the plate are exactly satisfied. Even for a complicated loading, when the non-uniform normal and shear loads are imposed simultaneously on the top and bottom surfaces of plate and transverse stresses boundary conditions on these surfaces are non-zero.