A numerical procedure is presented for predicting the static and dynamic aeroelastic characteristics of thin, clean swept wings in transonic flow. The method is based upon the simultaneous time integration of the equations governing the coupled nonlinear fluid dynamic and structural aeroelastic system. Governing equations for the system are developed and the numerical algorithm, including the coupling procedure for their solution, is discussed. As a computational example, the flutter of a simple rectangular wing is considered. Solutions are presented for a range of Mach numbers and dynamic pressures and compared to other existing flutter analysis methods including doublet lattice, modified strip theory, and time linearization. Unlike other procedures, the method presented here is capable of predicting the nonlinear interaction between unsteady shock wave motions and the dynamic response of an elastic wing. Computed results indicate the existence of the "transonic bucket."