Abstract This paper presents a mathematical study on the subsonic aerodynamics acting on an airfoil with a cubic stiffness. One portion of aerodynamics is assumed as and replaced by an equivalent damping. Using the harmonic balance method, an equivalent system is deduced and studied by a numerical integration method. Numerical examples show the validity and feasibility of the proposed mathematical treatment of the aerodynamics. It reveals that the unsteady aerodynamics acting on the airfoil can not only affect the pitch stiffness but also result in additional damping.