Evaluation methodologies for the flow-induced vibration of an elastic beam subjected to an axial flow confined in a narrow passage are reported. In this paper, by using the analytical method already proposed by one of authors, a parameter study is performed on the dynamic stability of an elastic beam subjected to axial flow confined a narrow passage. The effects of support conditions of structures, structural damping, and fluid characteristics on the dynamic stability are clarified. Especially, paying attention on the vicinity of critical velocity, the effects of stabilization or destabilization on flutter and divergence are investigated by changing fluid viscosity and structural damping.