V.Z.Vlasova variational method in displacements obtained ordinary differential equations for the anisotropic membrane cylindrical shell with the stringers. The differential equation for the construction of a complete system of orthogonal eigenfunctions of an arbitrary cross-sectional contour of such a shell. When you use these functions and their derivatives in the expansions for the longitudinal and transverse displacements equation method V.Z.Vlasova break and solved exactly. Examples of such exact solutions.