The e!ect of inviscid plug #ow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The #uid-structure systems consist of plates and membranes with bounded and unbounded #ow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel #ow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin}Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the in#uence of #ow velocity, con"nement and structural sti!ness on the existence of absolutely unstable waves in inviscid hydroelastic systems.