Summary: This paper is concerned with correspondences and analogies between flexural vibrations of shear-deformable layered beams or plates and solutions for homogeneous structures rigid in shear. The first-order Timoshenko-Reissner-Mindlin kinematics is applied to the laminate overally or layer-wise. Geometrically linearized vibrations of beams with various boundary conditions and of plates with arbitrary polygonal shape and hinged boundary conditions are discussed, together with physically nonlinear vibrations of beams and geometrically nonlinear vibrations of plates.