The aeroelastic stability of an orthotropic panel in a duct with rectangular cross section is examined. The panel extends along the flow direction in the duct which is infinite in length. The panel vibration is modeled by linear plate theory and the flow in the duct is modeled by the compressible linearized potential theory. The panel is placed in the mid-section of the duct and is simply supported at the sides. The material of the panel is assumed to be orthotropic. This would model, for example, unidirectional fibers placed in an isotropic plate, either along or perpendicular to the flow direction. An analytical solution is given for the eigenvalues of the panel vibration and results are presented for a range of parameters in the problem.