Several types of artificial muscles are actually able to mimic the active spring-like behaviour characterizing the tension-length diagram of the skeletal muscle but the natural damping expressed by the typical tension-velocity Hill’s relationship is not so easy to integrate in a simple way into the artificial muscle functioning. We discussed the use of a textile braided sheath, particularly in the case of the so-called McKibben structure to obtain a Hill’s model-like dynamic behaviour of the artificial muscle. Experiments are reported to compare “quick-release” experiments – as defined in muscular physiology – between artificial muscles whose braided weave is made of metallic strands and of rayon textile strands. It is shown that only in the second case a typical hyperbolic tension-velocity is highlighted with a curvature close to this of human skeletal muscle. It is also shown how the typical laws of friction in textile can explain this analogical behaviour with the Hill’s-model interpreted as a force model including a typical non-linear viscous component. An original interpretation of Hill’s model in terms of natural load-variations adaptation is given and so the advantage for an artificial muscle to get this biomimetic character.