The evaluation methodologies for the flow-induced vibration of an elastic beam subjected to an axial flow in confined narrow passage are reported. One of authors has already proposed an analytical method using the Navier-Stokes equation for the dynamic stability of an elastic beam subjected to an axial flow confined in a narrow passage. In this paper, by using the proposed analytical methods, the numerical studies are performed taking three kinds of support conditions as parameters, that is, a cantilever fixed at the upstream side, a cantilever fixed at the downstream side, and a simple support beam at the both sides, respectively. Moreover, the parameter-studies are also performed concerning with a width of annular gap, viscosity of a fluid, and structural damping. And the effects of support conditions of a structure, structural damping, and fluid characteristics on the dynamic stability of an elastic beam due to an axial flow confined in a narrow passage are clarified for proposing a safety dynamic design guideline concerning axial flow-induced vibrations in industries.