Summary: The effect of random variation of in-plane load acting on panels in supersonic flow is examined. The analysis includes stochastic stability and response moments of linear and nonlinear panels. The response moment equations are generated by using the Fokker-Planck equation approach. The mean-square stability boundaries and response moments are determined as functions of the spectral density of in-plane loads, aerodynamic pressure, air-to-structure mass ratio, and structural damping ratios. The nonlinear response is estimated by using a cumulant-neglect scheme. For equal modal damping coefficients, it is found that the damping stabilizes the panel in the sense of mean square. However, a paradoxial effect of the damping is found only for unequal damping coefficients where the effect is nonbeneficial. This observation is identical to the well-known results pertaining to the deterministic theory of panel flutter. The nonlinear response statistics are obtained in the time domain, the steady-state reveals that the response process is strictly stationary. This feature is believed to be first known for coupled systems with stiffness nonlinearity and is contrary the nonstationary response characteristics of dynamic systems with inertia nonlinearity.