Abstract: Small longwave free bending vibrations of a multilayered plate with alternating rigid and soft layers are considered. Approximate ways of determination of the transversal shear flexibility necessary when replacing a multiplayer plate by an equivalent single-layered Timoshenko–Reissner plate are discussed. A comparison with the exact solution of the three-dimensional problem of the theory of elasticity is performed. The dependence of shear flexibility and vibration frequencies on the ratio of Young’s moduli of the layers and their arrangement is investigated.