This paper focuses on the fretting fatigue behaviour of pin-loaded carbon-fibre-reinforced polymer (CFRP) straps studied as models for rigging systems in sailing yachts, for suspenders of arch bridges and for pendent cables in cranes. Eight straps were subjected to an ultimate tensile strength test. In total, 26 straps were subjected to a fretting fatigue test, of which ten did not fail. An S–N curve was generated for a load ratio R of 0.1 and a frequency f of 10 Hz, showing a fatigue limit stress of the straps around the matrix fatigue limit, corresponding to 46% of the straps’ ultimate tensile strength (σ_UTS). The fatigue limit was defined as 3 million load cycles (N = 3 × 10⁶), but tests were even conducted up to N = 11.09 × 10⁶. Catastrophic failure of the straps was initiated in their vertex areas. Investigations on the residual strength and stiffness properties of straps tested around the fatigue limit stress (for N ≥ 1 × 10⁶) showed little influence of the fatigue loading on these properties. Quasi-static finite element analyses (FEA) were conducted. The results obtained from the FEA are in good agreement with the experiments and demonstrate a fibre parallel stress concentration in the vertex area of factor 1.3, under the realistic assumption of a coefficient of friction (cof) between pin and strap of 0.5.