Determination of hyporheic zone thickness in streams is an important step for study of stream-aquifer interactions. Knowledge about hyporheic zone thickness is useful in stream restoration. However, because there is a lack of standard techniques for such study, evaluation of the hyporheic zone thickness for a given stream reach remains a challenge task for researchers. This paper presents Galerkin finite element flow and stream function models that can simulate the hyporheic zone thickness. The flow and stream function equations are solved for 2-D profile domains that can be across a stream or parallel to a stream. The numeral schemes for solving the flow and stream function equations and the treatment of boundary conditions are described. Hypothetical streams are used for simulation of the control of hyporheic zone thickness by the magnitude of inflow and outflow that occur at the stream-sediment interface. Groundwater flow velocity field is generated to examine the flow dynamics in hyporheic zones. The magnitude of groundwater flow velocity in hyporheic zone is greater than that of regional groundwater flow.