The existing flexible cable dynamics model, established using the absolute nodal coordinate formulation (ANCF), suffers from the issue of strain coupling. It also does not consider the nonlinear mechanical properties inside the flexible cable and consequently provides an inaccurate description of the strain and the constitutive properties. In this study, the axial strain of the flexible cable was redescribed by constructing an equivalent rod element in order to decouple the axial strain and bending strain. Subsequently, a strain-decoupled ANCF cable element was derived. Then, by analyzing the geometry of the stranded flexible cable as well as the relative sliding and friction between the wires in the cable, the axial stiffness and bending stiffness calculation formulae were obtained and the decoupled-stranded model was established. This study, therefore, achieved an improvement upon the traditional model in describing the strain and constitutive properties. The simulation results show that the decoupled model eliminates the strain coupling effect compared with the traditional model and has the advantages of fast convergence and high accuracy. The stiffness characteristics analysis shows that the bending stiffness of the cable changes during the bending process due to the relative motion and friction between the wires. Finally, the comparative analysis shows that the accuracy of the decoupled-stranded model is very close to that of the detailed model and performs much better than the other ANCF models, and the complexity of the decoupled-stranded model is far lower than that of the detailed model.