This paper describes computational work to understand the unsteady flow-field of a shock wave discharging from an exit of a duct and impinging upon a plate plane. A flat plate is located downstream, and normal to the axis of the duct. The distance between the exit of the duct and flat plate is changed. In the present study, two different duct geometries (i.e., square and cross section) are simulated to investigate the duct geometry effect on the unsteady flows of a shock wave. In computation, the TVD scheme is employed to solve three-dimensional, unsteady, compressible Euler equations. Computations are performed over the range of shock Mach number from 1.05 to 1.75. The results obtained show that the pressure increase generated on the plate by the shock impingement depends on the duct geometry and the distance between the duct exit and plate, as well as the shock Mach number. It is also found that for the duct with cross-section, the unsteady loads acting on the plate are less, compared with the square duct.