The frictional damping properties of axially loaded simple straight wire rope strands are studied using an analytical model for cables of current design. Since the cable axial response is driven by the interwire local pivoting, a first linear model is built in which pivoting occurs without friction. A hysteretic model is then built after a specific law of friction is established. Using comparisons with experimental results described in the literature, the frictional energy dissipated over a load cycle is shown to be very small compared to the elastic strain energy and other dissipations. This result is in agreement with the experimental fact that axially loaded simple straight strands do not experience fretting‐induced failures, except when they are close to the terminations.