Abstract: Based on the Kelvin-Voigt constitutive law, the governing equations for the fluRer vibration of the viscoelastic sandwich panel are established with consideration of the yon-Karmen thin plate large deflection and the nonlinear piston theory. By using the method of the Galerkin tnmcation, the nonlinear dynamical characteristics of the viscoelastic sandwich panel under the supersonic flow and with the simple suppoas on four sides are analyzed. For the equation of the first-order Galerkin truncation, the equilibrium of the system and its stability are studied, the critical flow of the static bifurcation is obtained; for the equation of the second-order Galerkin truncation, the critical flow of the Hopf bifurcation is obtained by applying the Hopf bifurcation criterion, the dynamical behavior with the varying flow conditions is observed by employing the diagram of the response and phase portrait.