This paper presents an extension of the simulation code ASWING to aeroelastic analysis of an airborne wind turbine. The device considered in this study consists of a tethered rigid wing with onboard-mounted wind turbines designed for wind energy harvesting in crosswind flight operation. The electrically conducting tether is deployed from a ground station and represented as a linear elastic spring with stiffness, mass, and frontal area emulating the properties of the real tether. The tether splits into several bridle lines to distribute the load transfer from the wing and to some degree also constrain its roll motion. The comparatively short bridle lines are considered to be inelastic with insignificant mass and aerodynamic drag contributions. The simulation model is validated by wind tunnel tests of a simplified scale model of the bridled wing. The comparison of computed and measured dynamic aeroelastic response shows that the tether force and the geometry of the bridle line system can strongly influence the flutter speed of the wing. In a final step, the simulation model is used to analyze the divergence, control reversal and effectiveness, and flutter behavior of a next-generation large-scale airborne wind turbine. The results confirm the significant influence of the geometry of the bridle line system on static and dynamic aeroelastic phenomena. It is concluded that classical methods used for suppression of aeroelastic instabilities can be applied to bridled wings only if this influence is taken into account.