The mooring lines of future floating wind turbines are typically composed of polymer fibre ropes (polyester, nylon, HMPE) and are traditionally connected to the platform with a steel chain. Given that chain failures are responsible for nearly half of all permanent mooring failures, Del Vecchio et al. (2024) put forward the suggestion of replacing the steel chain with a polymer fibre rope. However, it should be noted that maintaining tension in polymer ropes with a winch system can lead to abrasion and damage. A new solution, studied in the Velella project funded by the French government under France 2030, involves a textile chain made of HMPE fibres. This addresses challenges such as steel's weight and low oxidation resistance while mitigating rope abrasion issues. This innovative chain features a Möbius strip-inspired design, constructed from woven HMPE fibres. Recent studies by Y. Chevillotte, L. Civier and C. Bain have concentrated on visco-elasto-plastic (VEP) behaviour models for polymer ropes in marine environments and the measurement of friction coefficients between fibres. This is a crucial area of research for fatigue analysis in textile materials. A finite element model of the chain under tension is proposed, incorporating the strap's behaviour and a friction law governing strap-layer interactions. The aim of this model is to optimise winding parameters and improve mechanical performance, with a particular focus on the study of contact phenomena between chain links. The research results include key findings on the mechanical characteristics of the textile chain from strap tests, such as a negative Poisson's ratio and static/cyclic behaviour. Additionally, a finite element method determines the resting geometry of the link, with and without the Möbius twist, based on the strap's well-defined anisotropy directions. The next phase will integrate a VEP behaviour law for the strap to refine the finite element model further.