Abstract: A series of numerical computation have been conducted to characterize the movement of the terminal shock inside an axisymmetric supersonic inlet under different outlet conditions: sinusoidal perturbation pressure, experimental gauge pressure history at the head wall of a PDE and blockage of outlet of inlet. The relationship between the movement of terminal shock and the outlet conditions is demonstrated. The governing equations are discretized by finite volume method. The inviscid flux at the interfaces of control volumes is computed using three order upwind interpolation, while the corresponding viscous flux is computed using two order centered difference scheme. The minmod limiter is introduced to eliminate the non-physical elements of solutions. For steady computation, time-dependent method is used; for unsteady computation, dual time stepping method is used. The discretized algebraic equations are solved using alternate direction iteration method.