Stochastic stability of a viscoelastic plate in supersonic flow is investigated through both moment Lyapunov exponents and Lyapunov exponents, which are important indexes to characterize the moment stability and almost-sure stability of a stochastic dynamical system, respectively. The excitation is modelled as a bounded noise process. The plate is a typical example of a coupled non-gyroscopic system. By using the method of stochastic averaging, the equations of motion are decoupled into Itô differential equations, from which moment Lyapunov exponents are readily obtained. The Lyapunov exponents are obtained from the relation with moment Lyapunov exponents. Depending upon the relation among natural and excitation frequencies, parametric resonance can be categorized into no resonance, subharmonic resonance, combination additive resonance, and combination differential resonance. The diagrams of instability can provide insights on how to analyze and control parametric resonance in engineering applications.