The bending stiffness of a multilayer plate with alternating soft and hard layers is considered under the assumption that the deformation wavelength is substantially greater than the plate thickness. We discuss the approximate methods for determining the shear compliance required for replacing a multilayer plate with an equivalent single-layer Timoshenko–Reissner plate. A comparison is made with the exact solution of the three-dimensional problem of the theory of elasticity. The dependence of shear compliance on the ratio of Young’s moduli of layers and on their location is investigated.