The theory of plates finds many applications in civil, mechanical, aeronautical, and marine engineering, such as flat slabs in structures, waffle slabs, bridge decks, raft foundations, shear walls, pavements, folded plates, and sheet pile retaining walls. The development of plate bending theory occupied a central place in the history of engineering mechanics. In 1823, Navier derived the plate theory with the correct rigidity constant for the case of Poisson’s ratio being 0.25, and obtained the solution of a simply-supported rectangular plate in Fourier series. Reinforced concrete plates and wooden plates are inherently anisotropic, and anisotropic plate theory was considered by Gehring in 1877, Boussinesq in 1879, Huber in 1929, and Lekhnitski in 1968. The theory of plate bending without considering shear deformation is normally referred as Kirchhoff plate theory. For real plate applications, plates are often made of RC slabs, fiberglass panels, plywood slabs, and composite sandwich slabs.