Flap-bounding flight which is a flight mode consisting of continually repeated cycles with flapping and non-flapping phases is treated as a periodic optimal control problem. Two modelings of flap-bounding flight are developed. One modeling is based on energy consider-ations. The goal is to derive analytical solutions using an appropriate non-dimensionaliza-tion. The other model accounts for the unsteady behavior of the state and control variables. Furthermore, an efficient optimization procedure is used to construct solutions. It is shown where flap-bounding flight is superior in the required energy per range when compared to the best continuous flapping flight.