The author applies theoretical and numerical methods to study the wave-bearing behaviour of a finite flexible plate in a uniform flow under oscillatory excitation. It is found that the plate can respond to the frequences other than that of the driver; these frequences may either be present in the start-up procedure or be generated by wave conversions at the panel edges. At the first stage of evolution, two types of behaviour are possible which may be characterized as responses to low-frequency and high-frequency excitations. The first type exhibits spatially growing waves, and the second the absolute stability. The long-time behaviour of the flexible panel detects the growth of disturbance amplitude at all locations for flow speeds that vanish in the limit of infinitely long plate. The long-time growth of deformation in combination with low-frequency unstable waves is characteristic. The last waves are capable of convecting wall energy and thus the disturbance growth to all parts of the panel. At the later stages of the response, the line excitation is largely insignificant. The introduction contains a detailed survey of previous results on the problem.