Unbonded flexible pipes are widely utilized in the exploitation of offshore oil and gas resources. They are connected to two of the most critical types of system: floating production platforms and underwater production systems. However, if some tensile armor wires are substituted by cables or broken, the tensile armor layer will be incomplete, which seriously reduces the safety and reliability of the flexible pipe. In the present study, models of a flexible pipe with a complete tensile layer and with the tensile layer partially missing were established. The error for the tensile stiffness obtained by the finite element model of an intact flexible pipe was only 1% compared with experimental results. Because the load borne by the inner tensile armor layer is larger under tension than that borne by the outer tensile armor layer, the loss of inner tensile armor wires has a greater impact on the tensile properties. The maximum axial elongation of the flexible pipe increases with the number of missing inner tensile armor wires as a cubic polynomial. If the distribution of the missing armor wires is too dense, a stress concentration and local bending may occur, which will reduce the tensile strength of the flexible pipe.