On the basis of the linear theory of anisotropic laminated shells and the finite element method used to study the elastic deformation, stress state and strength of thin-walled curved tubes in pure bending. The pipe provided in the form of thin-walled toroidal shell with variable parameters and the wall thickness of the reinforcement. The calculation results are compared with those of known solutions and experiments. The dependence of the flexible pipe of the internal pressure, the geometric and structural parameters. The analysis of the strength of the multi-layer composite sample. Depending on the geometry of the structure of the package of layers and the reinforcement scheme is given a comparative analysis of the results.