In this paper, we analyze the flow regimes in an incompressible free-surface flow through porous media under unsteady flux inlet condition. There are two flow-regimes in the unsteady intrusion of water into porous strata. Initially, the flow is dominated by Inertia-Pressure (IP) regime then later by Pressure-Drag (PD) regime. The temporal powers for front position, flow depth and velocity derived for the backstep channel filled with porous media are compared with the results of numerical simulation and experimental observation. The results show a close agreement. We also carried out numerical simulations for an unsteady storage of stormwater into a granular sub-base from the side channel. The finite-volume method on a staggered grid is used as a basic scheme for numerical solution. The Cubic Interpolated Propagation (CIP) method is employed to solve the governing equations. The Volume Of Fluid (VOF) method is applied for free-surface tracking. The computed results for spatio-temporal evolution of fluid configuration and storage volume show the applicability of the model.