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Single-mode flutter is a type of panel flutter that occurs at low supersonic speeds without interaction between oscillation modes. In this paper, we investigate the single-mode flutter of thin elastic plates of different shapes exposed on one side to a perfect inviscid gas flow. We use the energy method in our study. Rectangular, trapezoidal, and parallelogram plates are considered. We obtained that the flutter boundaries for trapezoidal plates vary slightly in comparison with the rectangular plates. To the contrary, even at a small curvature angle the aeroelastic stability increases significantly for parallelogram plates.