Two-degrees-of-freedom, finite dimensional, nonlinear mathematical model, which models the nonlinear features of aircraft wing flutter in transonic speed is discussed. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear) flutter condition with its linear part. At a final procedure of improving a quantitative matching with the test data, the continuation method for analyzing the bifurcation is extensively used.