Abstract: The elliptic harmonic balance method is introduced to solve the nonlinear aeroelastic problem, and the flutter of 2-D airfoil with cubic nonlinear is studied. Firstly, the equilibrium equation of the nonlinear airfoil is established based on the first piston theory, and then solved with elliptic harmonic balance method. The validity of the analytical method is confirmed by comparing the Runge-Kutta (RK) solutions for various values of the vibrational amplitude. And the error is smaller than that of the harmonic balance method. A parametric study is carried out to study the influences of the position of elastic axis and the position of the center of gravity on the flutter velocity. The result shows that flutter velocity strongly depends on the position of elastic axis and the position of the center of gravity. The flutter velocity increases with the elastic axis closing to the airfoil midpoint. And with the center of gravity closing to the elastic axis, there is a minimum value of the flutter velocity.