Unbonded flexible risers (UFRs) connect surface production platforms to subsea production systems, and are therefore vital for tasks such as the transportation of oil and gas and the injection of water. The tensile armor layer is the main load layer of UFRs. Once this layer is partially broken, the safety of offshore oil and gas gathering and transportation is seriously threatened. In this study, an 8-layer UFR model is developed to calculate the effects of damaged inner and outer armor wires and boundary conditions on the tensile stiffness, ultimate load capacity, and stress distribution and load ratio of the inner and outer tensile armor layers. Broken inner tensile armor wires are found to have a greater impact on the tensile properties and produce the same torsional buckling failure mode as observed in the field. The influence of the pressure load on the ultimate load capacity of the UFRs is analyzed, and the results demonstrate that the outermost pressure increases the interlayer action between the tensile armor layers and the adjacent layers, thereby reducing the torsional angle of the UFRs under the ultimate tension. Additionally, the innermost pressure is found to have a negligible effect on the ultimate load.