Flying insects, such as dragonfly and butter fly, are known to have the flapping mechanism which is essentially based on the resonance of thorax excited by attached muscles. In this study, the flapping motion is modeled as the second mode vibration of a ring with a pair of wings attached to the vicinity of two neighboring nodal point, so that the angular motion of the wings can be maximized. In addition to the lift gained by the mechanism, the capability of self-attitude control of the flapping mechanism is investigated when it is inclined from its equilibrium due to external disturbances. Simulation results show that the self-attitude controlled flapping mechanism can be either stable or unstable, depending upon the attachment locations of the wings. Experimental works are also performed to verify the theoretical findings.