In this work we carry out a numerical study of the influence of the upstream Mach number on the flutter of a three-dimensional, cantilevered, flexible plate subject to a subsonic, inviscid, open flow. We have assumed a linear elastic model for the plate and that the fluid flow is governed by the linearized potential theory. The fluid equations are solved by means of a doublet point method to obtain the generalized aerodynamic forces as a function of the plate displacements. Then, these generalized forces are coupled to the equation of motion of the plate, which is discretized with a spectral Galerkin method, and an eigenvalue analysis is performed to find the flutter point. The obtained results are in good agreement with those of related theoretical and experimental studies found in the literature.