Airborne Wind Energy (AWE) is a promising new technology, and attracts a growing academic and industrial attention. Important research efforts have been deployed to develop prototypes in order to test the technology, generate control algorithms and optimize the efficiency of AWE systems. By today, a large set of control and optimization methods is available for AWE systems. However, because no validated reference model is available, there is a lack of benchmark for these methods. In this paper, we provide a reference model for pumping mode AWE systems based on rigid wings. The model describes the flight dynamics of a tethered 6 degrees of freedom (DOF) rigid body aircraft in form of differential-algebraic equations, based on Lagrange dynamics. With the help of least squares fitting the model is assessed using real flight data from the Ampyx Power prototype AP2. The model equations are smooth and have a low symbolic complexity, so as to make the model ideal for optimization and control. The information given in this paper aims at providing AWE researchers with a model that has been validated against flight data and that is well suited for trajectory and power output simulation and optimization.