One of the keys to realistic mathematical modelling of any transport phenomenon is to understand the fluid mechanics of the process correctly. However, this is a daunting task for the subsurface flow systems: the geometry of the domain is irregular, the physical/structural characteristics are not known with certainty and, to make the problem further complicated, the processes often involve combined free and porous flow regions. Modelling for combined free and porous flow under the ground is of significant practical importance in many areas of water resources engineering. These include, for example, water seepage and contaminant mobility through preferential flow channel boundaries, groundwater rise and fall and flow circulation in the subsurface, permeable reactive barrier technology and many other important transport processes. The presence of impermeable or multiple number of permeable interfaces in the physical domains of the combined free and porous flow sections and the aspect ratios between the sub-domains may also significantly influence the fluid dynamics in such coupled systems.