The paper is concerned with a thin beam and a thin plate made of a transversally isotropic linearly elastic material heterogeneous in the thickness direction. The ordinary Kirchhoff–Love and Timoshenko–Reissner models are known to be unacceptable for a strongly heterogeneous material or for a multilayered material with large ratio between the Young moduli of layers. A generalized Timoshenko–Reissner model is proposed for bending and free vibrations of such beams/plates. A multilayered beam/plate is reduced to one‐layer one with the equivalent elastic parameters. The range of application of such a model is very wide.

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The 2D Kirchhoff–Love (KL) theory and the Timoshenko–Reissner (TR) theory for thin shells made of the transversally isotropic, homogeneous material are discussed. For the cyclic‐symmetric deformations of shells of revolution the asymptotic analysis of stress–strain states is performed. Two simple linear problems for double‐periodic deformations of plates are studied applying the exact 3D theory and the 2D approximate theories. From these problems it follows that the KL theory is asymptotically correct because it gives the first term of asymptotic expansion of the 3D solution. The TR theory is asymptotically incorrect. It gives correctly the first term only and incorrectly the second term. But if the transversal shear modulus is comparatively small then this theory gives the main part of the second term. The case of the extremely small shear modulus is discussed. As an example the multi‐layered plate with alternating hard and soft isotropic layers is studied.

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