By numerically solving elementary aeroelastic models, the response of aeroelastic systems can be simulated and studied under various conditions. This provides a deeper understanding of how aerodynamic forces, structural deformations, and vibrations interact and influence the system’s stability. It is essential to recognize that aeroelastic systems can exhibit changes in their stability characteristics due to factors such as flight conditions and structural and aerodynamic modifications. Moreover, the energy flow during the instability is investigated for the typical section. The flutter phenomenon and the classical tools for its prediction are presented.