This Study focuses on the bending performance and cross-sectional deformation of reinforced thermoplastic pipes (RTPs) used in offshore oil and gas transmission. Based on the nonlinear cylindrical shell theory, the elliptical deformation of the RTPs’ cross-section is parametrically analyzed, the geometric equations for the deformation of the flexible pipe are derived, and the principal structure equations of the flexible pipe are established considering the material nonlinearity and failure criterion of the composite materials. Further, the nonlinear equations of RTPs in equilibrium at any loading moment are established by combining the geometric equations, intrinsic constitutive equations and applying the principle of virtual work, and the equations are solved numerically by Newton's iterative method to complete the establishment of the three-dimensional theoretical analysis model of RTPs under pure bending. The model is validated through mechanical property tests. Buckling stress analysis, failure mode analysis, and stiffness degradation analysis are conducted to investigate the stress distribution, bending failure mechanism. The study identifies five failure modes under pure bending conditions and presents a four-stage degradation process of RTPs’ stiffness. It contributes to understanding the behavior of RTPs under pure bending loads and provides insights for improving the design and reliability in offshore applications.