Combining the curvature concept in mechanics of materials with the Grossman theory to calculate the aeroelastic force, the nonlinear dynamic model of high-aspect-ratio wings was established by using Lagrange equation. The model was rewritten as dimensionless equations. The critical conditions and route for the stable solution to Hopf bifurcation solution were investigated by using the first Lyapunov quantity. The identification conditions for benign flutter and catastrophic flutter were obtained. The flutter is benign when the first Lyapunov quantity is negative, while the flutter is catastrophic when the first Lyapunov quantity is positive. The flutter was also studied by the normal form theory and Hopf bifurcation theory. The influence of different aspect ratio on the flutter speed was investigated. The results show that the flutter speed first decreases, then increases, and at last decreases as the aspect ratio increases. The Numerical Simulations were also given, which verify the analytical results.