This paper presents a multibody approach to dynamics modelling of a variable-length tether moving through air, in a system where an airborne module generates aerodynamic lift and uses the tether to cyclically drive the winch-generator unit fixed on the ground. The rope is modelled as a series of straight, massless, elastic segments with the rope mass fragments lumped to the segment joints. Individual segment length is constant, with the exception of segment being wound out from the winch, while the number of segments is variable. For the segment being wound out, a special modelling approach is derived. The forces acting on the rope are also concentrated at the joints, thus simplifying computations and facilitating rope aerodynamic drag modelling. The proposed tether dynamics model is integrated into the overall model of controlled power production system and verified by computer simulation. The model is compared with two simpler tether dynamics models also proposed in the paper.