A thin linearly elastic shell made of heterogeneous anisotropic material is studied. The general anisotropy described by 21 elastic moduli is examined. The material may be functionally graduated or multi-layered. The asymptotic expansions in powers of the relative shell thickness of the three-dimensional elasticity equations are used to deliver the two-dimensional shell model. In the zeroth-order approximation the model of 8th differential order is obtained. The asymptotic precision of this model is the same as the precision of the classic Kirchhoff-Love model for isotropic shell. Influence of the elastic moduli variation in the thickness direction is examined. As an example the Donnell system for shallow shells is presented, and this system is used to discuss the free transversal shell vibrations spectrum.