This paper conducts delayed detached eddy simulation of a supersonic panel vibration at Mach 2.0. Unsteady 3D compressible Navier-Stokes equations are solved with a system of 5 decoupled structure modal equations in a fully coupled manner. The low diffusion E-CUSP scheme with a 5th order WENO reconstruction for the inviscid flux and a set of 2nd order central differencing for the viscous terms are used to accurately capture the shock wave/turbulent boundary layer interaction of the vibrating panel. The shock waves and their reflection interacting with turbulent boundary layer in the tunnel are well captured by the DDES. The panel vibration induced by the shock boundary layer interaction is well resolved by the simulation. The panel response agrees well with the experiment in terms of the mean panel displacement and frequency. Since it is a fully coupled fluid-structural interaction simulation, the flow and structure responses are captured by the solver itself with no parameter adjustment. The simulation is fairly efficient due to the high order schemes. It takes one week wall clock time to run 0.1s physical time with 264 CPUs using parallel computing.