Unsteady shock wave propagation through ducts has many applications, ranging from blast wave shelter design to advanced high-speed propulsion systems. The research objective of this study was improved fundamental understanding of the transient flow structures during unsteady shock wave propagation through rectangular ducts with varying cross-sectional area. This research focused on the fluid dynamics of the unsteady shock-induced flow fields, with an emphasis placed on understanding and characterizing the mechanisms behind flow compression (wave structures), flow induction (via shock waves), and enhanced mixing (via shock-induced viscous shear layers). A theoretical and numerical (CFD) parametric study was performed, in which the effects of these parameters on the unsteady flow fields were examined: incident shock strength, area ratio, and viscous mode (inviscid, laminar, and turbulent). Two geometries were considered: the backward-facing step (BFS) geometry, which provided a benchmark and conceptual framework, and the splitter plate (SP) geometry, which was a canonical representation of the engine flow path. The theoretical analysis was inviscid, quasi-1D and quasi-steady; and the computational analysis was fully 2D, time-accurate, and viscous. The theory provided the wave patterns and primary wave strengths for the BFS geometry, and the simulations verified the wave patterns and quantified the effects of geometry and viscosity. It was shown that the theoretical wave patterns on the BFS geometry can be used to systematically analyze the transient, 2D, viscous flows on the SP geometry. This work also highlighted the importance and the role of oscillating shock and expansion waves in the development of these unsteady flows. The potential for both upstream and downstream flow induction was addressed. Positive upstream flow induction was not found in this study due to the persistent formation of an upstream-moving shock wave. Enhanced mixing was addressed by examining the evolution of the unsteady shear layer, its instability, and their effects on the flow field. The instability always appeared after the reflected shock interaction, and was exacerbated in the laminar cases and damped out in the turbulent cases. This research provided new understanding of the long-term evolution of these confined flows. Lastly, the turbulent work is one of the few turbulent studies on these flows.