For the purpose of ultimately building a fully dynamic simulation of kites, an investigation is launched into a viable model of the cable with which the kite is attached to the ground. In the model proposed in this paper, only the slow modes of motion are taken into account due to the fact that only the slow motions have a real effect on the flight characteristics of the kite. Fast vibrations have a low amplitude with little effect. Also, by taking out all the fast modes of motion, the time step for integration can remain fairly large, speeding up the calculation process. Of special interest in the model is the damping which consists of aerodynamic damping and material-based damping. The relation between these two forms of damping is investigated. Verification of the model is done through comparison with analytical and real-life measured data. The resulting model is simulated in MSC ADAMS. It is shown that the aerodynamic damping is of prime interest because it dampens the slower motions. Material damping dampens mostly the fast vibrations.