There are very few precise and reliable solutions available in the existing literature for functionally graded plates with fully clamped ends under mechanical loads, indicating a significant research gap in this area. In this article, an analytical solution for clamped functionally graded plates subjected to mechanical load is introduced. The shear deformation theory, governing equations, and boundary conditions are derived based on the Carrera Unified Formulation (CUF) strategy, and the solution is obtained by using the boundary-discontinuous Fourier method. The mechanical properties of the plates are assumed to vary according to an exponential law and a power-law distribution along the thickness direction in terms of the volume fractions of the constituents. The results presented in this article cover a large spectrum of plate thicknesses, ranging from thick to thin, and encompass various values of the functionally graded parameter. Accurate results of shear deformation theories with various order of expansion are achieved. Finally, a gap in the literature is covered and benchmarks solution are provided.