Abstract: A computational aeroelasticity method based on unstructured grids was developed to study fluid/structure interaction problems.The aerodynamic model was used for solving the compressible Reynolds average Navier-Stokes equation on moving grids.A nodal-centered finite volume method with mixing unstructured grids was adopted to handle the complex fluid/structure problems.The structure vibration was modeled by a linear model.The structure deformation due to the aerodynamic loading was approximated by solving the structure dynamic equation and projected to the aerodynamic domain by grid deformation method.This method was validated by solving a harmonic pitching airfoil and used for numerically simulating the flutter boundary of the AGARD 445.6 wing.