Based on the energy method, the trim equations of flexible aircraft considering static aeroelasticity are derived. The idea of using static vortex lattice method combined with Trefftz plane theory and empirical formula to solve the induced drag and trim drag of flexible aircraft in trimmed level flight was proposed. The method of reducing total induced drag through optimization of the wing geometric twist angle was introduced. An UAV with twin tailbooms was analyzed. The result shows that the longitudinal bending stiffness has large effects on the total induced drag of the aircraft in such configuration, and it also affects the profile drag of the elevator deflexion and the total drag of the aircraft remarkably. Results of the optimization indicate that appropriate optimization of the geometric twist can make the whole span-wise lift distribution more close to the ellipse one, which will reduce the total induced drag effectively and other drag components positively.