In practical applications, sandwich plates are often connected to other members, supported by damaged clamped/simply supported boundary conditions or supported by elastic restraints. Therefore, the mentioned structures may not always be simulated by the classical boundary conditions, i.e., ideal simply supported, clamped and free edges. Also, these structures may be subjected to various loads. In this study, for the first time, a novel economical analytical solution procedure is presented for axisymmetric static analysis of sandwich annular plates, by using the layerwise and 3D elasticity theories. Based on the proposed approach, functionally graded sandwich annular plates with various elastically restrained edges under arbitrary distributed loads may be analyzed and all of the displacements and stresses components may be exactly achieved. Also, imposed loads at the boundaries may be evaluated. Transverse shear and normal stresses boundary conditions on the top and bottom of the sandwich plate and the interlaminar continuity conditions of the in-plane displacement, transverse shear and normal stresses are exactly satisfied. Accuracy and efficiency of the presented solution procedure are demonstrated by comparing the obtained results for sandwich plates with the classical edge conditions as some special cases of the elastic supports with results of the three-dimensional theory of elasticity.