This paper presents a numerical study of the dynamic response and stability of a partially confined cantilever pipe under simultaneous internal and external axial flows in opposite directions. The onset of flow-induced vibrations is predicted by the developed numerical model, and moreover, limit-cycle motion occurs as the flow speed becomes larger than a critical value. The numerical results are in good agreement with existing experimental results. The simulation gives control over many physical parameters and provides a better insight into the dynamics of the pipe. A parametric study regarding the stability of the system for varying confinement length is performed. The current results show that there is an increase in the susceptibility of the system to instability as the extent of confinement is increased.