The paper deals with a thin shell made of transversely isotropic linearly elastic material. The material is supposed to be strongly heterogeneous across the thickness. The shell may in part be multilayered of functional gradiation. A shallow shell model taking into account the transversal shear is proposed to approximately solve some shell problems. The model combines the shallow model of the Mushtary-Donnell-Vlasov-type and theTimoshenko-Reissner shear model. This model proves useful in finding the shell deflections and in solving some vibration and buckling problems. On the other hand, this model is useless if the aim is the stress distribution in the thickness direction. The model accuracy is estimated by comparison with some test problems for which the 3D equations of the theory of elasticity have exact solutions. In particular, it turns out that the model is acceptable for a three-layer circular cylindrical shell with the contrast of the Young moduli being 1000.