The Shear Stress Transport model based improved delayed detached eddy simulation of the AGARD Wing 445.6 is performed at the subsonic, transonic and supersonic flow with high order shock capturing schemes. An implicit unfactored Gauss-Seidel line iteration scheme is used to solve the compressible, filtered Navier-Stokes equations. The flow solver and the modal form structural solver utilize the dual time-stepping scheme to achieve fully coupled fluid-structural interaction via successive iterations using a pseudo time step. The LES sub-grid length scale based on the vorticity aligned with a grid line is used to overcome the standard sub-grid length scale’s delayed flow transition problem. The predicted flutter boundary agrees well with the experiment at different Mach numbers, including the supersonic flow where the traditional RANS methods over-predict the flutter velocity index and frequency. At the transonic and supersonic flow, the torsional mode generalized displacement is decreased due to the shock oscillations over the suction and pressure surface of the wing. At the flutter boundary, no flow separation is observed at different Mach numbers.