Two-dimensional model of shell made of an anisotropic material described by 21 elastic moduli is delivered. It is shown that, in the general case (in contrary to isotropic or orthotropic materials), both the Kirchhoff-Love and the Timoshenko-Reissner hypotheses result in 2D models, which are inconsistent in the major terms with respect to the small thickness parameter equal to the ratio between the thickness of shell and the wavelength. For this aim the generalized Timoshenko-Reissner hypothesis is proposed. The asymptotic analysis of the obtained 2D shell model is used to investigate the cylindrical shell free vibrations. The main types of the vibration modes are described and they are compared with the modes of the isotropic shell. The membrane modes are investigated. The system of Donnell type is delivered. This system is used to investigate free vibrations of a circular cylindrical shell. The example of material with the general anisotropy is given.