The use of coupled models of hydrologic analysis, which includes more than one component of the hydrologic cycle, is a common occurrence. Coupled models tend to be more complex and their solution may suffer numerical complications. In this study, we present a coupled hydrological model to simulate the interaction between stream flow and groundwater flow. A one-dimensional stream flow model using the complete form of the St Venant equation is coupled with a two-dimensional vertically averaged groundwater flow equation in an unconfined aquifer. The governing equations of the two different hydrological domains are linked with the recharge term at the river bed. The resulting coupled mathematical model is solved simultaneously by linking the two hydrologic system matrices in a global matrix. The proposed simultaneous solution approach provides a more efficient solution for the coupled flow problem and is superior to the approximate solution obtained through an iterative approach.