Accompanying with the improvements in design technology and application of advanced materials, the structure of modern aircraft is much lighter and more flexible, which induced significant aeroelastic effects. Decoupling of the rigid-body motion and the elastic vibration is not always present. As a result, this dissertation works in the interdisciplinary field of flight dynamics and aeroelasticity to search for an integrated flight dynamic modeling methodology for flexible aircraft. The Lagrange equations of motion of the flexible aircraft are derived, which considered the rigid-body degrees of freedom and elastic degrees of freedom. With the assumption of small disturbance on the nonlinear trim equilibrium state, the state-space equations describing the motion with rigid-body degrees of freedom and elastic degrees of freedom are established. The unsteady aerodynamics in the frequency domain is computed by the doublet-lattice method, and then it is transferred into the time domain by the rational function approximation. The state-space equations are applied to analyze the stability of the very flexible aircraft, and the results are compared to the rigid method and linear method, in order to illustrate the effects of geometric nonlinearity and the coupling between rigid-body motion and elastic vibration. The results of nonlinear analysis indicate that the critical stability flight speed is even lower than the result of linear analysis.