Abstract: For flow around airfoil with local elastic structure at low Reynolds number, the unsteady flow separation excited by the self-induced oscillation of local elastic structure has been analyzed in detail. The arbitrary Lagrangian Eulerian-characteristic-based split (ALE-CBS) scheme is developed to simulate the flow field with moving boundary. Moreover, Galerkin method is used to approximate the governing equations of the local elastic structure. The analysis is focus on the influences of the local elastic structure on the flow separation and airfoil performance. Further, different unsteady separation phenomena are studied from both Eulerian and Lagrangian viewpoints. The results show that local elastic structure of airfoil has significant effect on the unsteady separation and streamline structure, and can enhance the lift performance by the moving separation on airfoil surface, resulting in reattachment. Compared with Eulerian description, the Lagrangian description of separation can reveal the nature of lift enhancement and momentum transfer from main flow to boundary.