The 2D Kirchhoff-Love (KL) theory and the Timoshenko-Reissner (TR) theory for thin shells made of the transversally Isotropie, 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.