The wave propagation in cylindrical shell under the influence of the different factors, such as visco-elasticity, magneto-elasticity, presence of temperature field and fluid, the layerness and anisotropy of the shell is a very interesting problem. Composite materials posses different properties, giving a push to further development of the theory of elasticity of anisotropic bodies, in particular theory of anisotropic plates and shells. For different thin shells, made from different materials, based on dispersion equations received dependencies of wave velocity to the angle between physical and geometrical axes of the shell are constructed. Anisotropic shells, containing fluid: compressed and incompressible, are considered. Constructed the surfaces, showing change of velocities depending on angle between physical and geometrical axes of shell and length of wave. Comparison of all received results is resulted which reveals the stabilizing role of fluid. The behavior of three layered orthotropic shell on the example of arteries is investigated. On the same example comparison with the similar shell is resulted and analysis of this comparison is given. Analysis shows that the velocity in a layered shell much more decreases in comparison with one layered.