We study the time-harmonic resonance of a finite-length elastic plate in a fluid in 5 uniform flow confined in a duct. Although the resonance frequencies are usually real, the combined 6 effects of plate elasticity and of a flow can create complex frequencies, different from the usual so-7 called scattering frequencies, corresponding to instabilities. We study theoretically the existence of 8 instabilities versus several problem parameters, notably the flow velocity and the ratio of densities 9 and of sound speeds between the plate and the fluid. A 3D-volume in the parameters space is defined, 10 in which no instability can develop. In particular it corresponds to a low enough velocity or a light 11 enough plate. The theoretical estimates are validated numerically. 12