A pumping kite system is a new innovative way to generate sustainable energy. A large kite is used to generate a pulling force which is transmitted to the ground by a tether. The tether is reeled off a drum that is connected to a generator. When the tether is completely unwound the kite is controlled in such a way it hovers down like a parachute, with almost no traction force, and the tether is reeled-in. This results in a cycle which produces a net amount of energy. Currently multiple institutes and companies are investigating and developing such pumping kite systems, including the ASSET institute at the TU Delft. A simple, realistic and fast kite model is essential during the development of these systems. Such a model could be used for: estimation of the power production, structural optimization, trajectory optimization and for example autopilot development. This thesis describes the development of a realistic real time capable pumping kite model. Initially a literature study gives an overview of the current models available in literature. It explains the advantages and shortcomings of the different approaches. Main shortcoming of most kite models is their limited validation. As a result their accuracy is unknown. Secondary, the measurement data of a 20kW prototype, which has been developed by the ASSET kite group, is used in an extensive data analysis and system identification. The general dynamics are described and multiple relevant phenomena are found. Especially the rotation of the kite has been studied. An useful relation is found which couples the rotation of the kite to the steer input and the side slip angle (or gravitational vector). This relation originates from a moment study of the kite on a quasi-static basis and corresponds with measurement data. Further the sagging of the tether due to tether drag and pod dynamics has been studied. Relatively small sag angles of 0-150 are found during regular flights and a characteristic pattern indicates that especially the pod dynamics play a role in the flight dynamics. Finally the aerodynamic forces acting on the kite have been studied and coefficients needed for an aerodynamic force model have been fitted to the measurement data. It is concluded, based on the literature study and data analysis, that a semi-rigid body modelling approach is most suited. The semi-rigid body model simulated the kite as a point mass with one additional degree of freedom, namely the rotation of the kite around the tether (yawing of the kite). The pitch angle of the kite, which is adjustable in the real system, is incorporated in the model by a variable constrain instead of an additional degree of freedom. The semi-rigid body kite model proves to be a simple and computer efficient model. The kite model is connected to two different tether models. A single spring-damper tether model which simulates the tether as straight and a discretised point mass model which is able to simulate the dynamics of the tether and pod. The kite model with both tether models have been validated by comparing the models to measurement data. Both models seem to realistically simulate the current kite system. The model with a straight spring damper tether model runs approximately 7x real time1 and correctly simulates all variables except the sag of the tether. The discretised tether model simulates these effect correctly but at the cost of simulation speed. Currently it runs approximately 0.5x real time. The discretised model additionally shows more realistic behaviour during non-normal flight conditions.