We present an analytical solution for the fully coupled structural-acoustic response of a thin elastic plate mounted in a rectangular duct assuming linear dynamics and acoustics. The plate is subjected to harmonic planar acoustic waves at grazing incidence in the presence of a subsonic uniform mean flow in the duct. Both clamped and simply-supported plates are considered. We identify regimes in which the structural-acoustic coupling plays a significant role on the response of the plate. Four metrics characterizing the coupled response are considered: the deviation of the peak response frequency from the in vacuo natural frequency of plate, the amplitude of the peak response, the effective acoustic damping of the plate, and the plate modal coupling through the duct acoustic field. The method is also used to estimate the onset of instability in the structural response of a duct-mounted clamped-plate with flow for estimating the range of applicability of the theory. For a typical aerospace structure, the panel-fluid coupling does little to change the fundamental vibration frequencies from their in vacuo values but significantly alters the amplitudes of the plate vibration. This is a result of the acoustic radiation being a strong function of the in-duct flow Mach number M∞. Further, the inter-modal coupling through the acoustic field is also a strong function of M∞. Therefore, reduced order models relying on the panel's in vacuo modes require Mach number-dependent coupling coefficients for accurate predictions.