Freeplay nonlinearity has been an obstacle hindering the development of active control system due to flutter. Analyzing the influence of freeplay nonlinearities on the vibration characteristics of a system is crucial for ad-dressing this challenge. This paper establishes a three-degree-of-freedom (3-DOF) two-dimensional (2D) wing model with control surface freeplay, which includes plunge, pitch, and control surface rotation degrees of freedom, to investigate the effects of freeplay on aeroelastic behavior. A time-domain computational method is derived to analyze the variation of the model's motion with respect to flow velocity. The computational results reveal two characteristic speed points that define the transition of the model's motion. At the first speed point, approximately 2.2 m/s, the motion transitions from convergence to divergence, eventually stabilizing into a limit cycle. This speed point represents the critical divergence speed when the torsional stiffness of the control surface is effectively zero, high-lighting the significant role of freeplay in altering the system's stability characteristics. At the second speed point, around 14.2 m/s, the motion transitions from stable limit cycle oscillations to complete divergence, representing the flutter critical speed of the system. Notably, this critical speed is consistent with that of the system without free-play, demonstrating that the presence of freeplay does not affect the ultimate flutter boundary but significantly in-fluences the transitional dynamics. These findings not only enhance the understanding of freeplay nonlinearities in aeroelastic systems but also provide valuable insights for the design and implementation of active flutter control strategies in practical engineering applications.