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The motion of a kite is simulated using an in-house numerical simulation code, where aerodynamics are coupled with flight dynamics. In the present study aerodynamic forces, attitude and stability are examined for a kite with camber and string lines. The results reveal that the kite shows stable flight; specifically, it keeps a constant altitude, moving from side to side periodically. The reason for this is the restoring forces produced by strings on the kite, which generate simple harmonic motion of the kite. The motion obtained by the present method shows good agreement with experimental results. Thus, the numerical method used here is found to be effective in the simulation of a kite. Furthermore, based on the data obtained from the present numerical simulation, a model is proposed to analyze the characteristic motion in the flight of a kite using its aerodynamic properties, and the period of the kite's periodical motion in the lateral direction is explained.