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To expand the application scope of prestressed carbon fiber-reinforced polymer (CFRP) cables in civil engineering, the ultimate tensile strength of these cables was tested and evaluated under bending conditions. First, the study analyzed the tensile failure mechanism of CFRP cables under bending conditions based on elastic bending analysis theory. Thereafter, the ultimate stress state of individual tendons and cables was derived and a calculation model for the tensile strength of bent CFRP cables was established. Second, 14 sets of test conditions were created for CFRP cables under bending angles of 20–40° and bending radii of 1.5–3 m. Then, bending tensile tests were conducted to evaluate the effects of the above factors on the ultimate tensile strength, and the correctness of the computational model was verified using experiments. Finally, the ultimate performance of CFRP cables was theoretically predicted using the established model. The results showed that the cable bending tensile strength was associated with the radius r, tensile strength f, and elastic modulus E of the reinforced material and the bending radius R, but was not correlated with the interface buffer material or the bending angle of the steering system. Moreover, the flexural tensile residual strength was only affected by R/r and E/f. When E/f involved conventional material parameters, the residual strength increased nonlinearly with increased R/r. When R/r ≥ 600, the residual strength reached more than 80%. Therefore, R/r at 600 could be used as the design basis for a safe critical radius. [ABSTRACT FROM AUTHOR]