The increasing number of applications involving the use of UAVs has motivated the research for design considerations that increase the safety, endurance, range, and payload capability of these vehicles. In this article, the dynamics of a flexible flapping wing is investigated, focused on designing bio-inspired UAVs. A dynamic model of the Flapping-Wing UAV is proposed by using 2D beam elements defined in the absolute nodal coordinate formulation, and the flapping is imposed through constraint equations coupled to the equation of motion using Lagrange multipliers. The nodal coordinate trajectories are obtained by integrating the equation of motion using the Runge–Kutta algorithm. The imposed flapping is modulated using a proposed smooth function to reduce transient vibrations at the start of the motion. The results shows that wing flexibility yields significant differences compared to rigid-wing models, depending on the flapping frequency. Limited amplitude of oscillation is obtained when considering a non-resonant flapping strategy, whereas in resonance, the energy levels efficiently increase. The results also demonstrate the influence of different flapping strategies on the energy dissipation, which are relevant to increasing the time of flight. The proposed approach is an interesting alternative for designing flexible, bio-inspired, flapping-wing UAVs.