The presented paper investigates the flutter phenomenon in a rectangular-shaped plate in supersonic air flow. First, the phenomenon of flutter and its identification method based on the analysis of eigenvalues are presented. Then, using the assumptions of Kirchhoff plate, the plate motion equation is derived and coupled with the first-order piston aerodynamic model. Next, the coupled structure-fluid equation is solved in matrix form using the differential quadrature method (DQM). Using the DQM numerical method in matrix form provides advantages such as high accuracy for solving the flutter problem. The obtained results show that the first phenomenon of flutter in an aluminum plate with a length and width of 1 meter and a thickness of 5 mm with clamped-free-clamped-free boundary conditions occurs in dimensionless dynamic pressure 617 (equivalent to Mach 3.395). The presented formulation can be used as a benchmark for solving and calculating the flutter speed of various objects in the supersonic air flow.