The need for robust modeling technology to address fundamental issues of water availability and water quality is becoming ever more pressing in view of increased pressures on water resources, restoration and maintenance of ecological systems, and uncertainties arising from climate change. Current models of conjunctive surface water flow in wetlands and groundwater flow in underlying aquifers, which are essential to the study of material and nutrient transport, appear to have some limitations and challenges. My research improves upon existing modeling technology in two main areas: (1) the development of improved analytic functions for transient groundwater flow or flow in aquifers underneath wetlands in the presence of leakage and (2) the development of a more stable and accurate modeling approach for conjunctive flow in wetlands and underlying aquifers by reformulating the problem in terms of discharge potentials. The new analytic functions are developed for use in the Analytic Element Method (AEM) and Laplace-Transform AEM, while the reformulation of conjunctive wetland and aquifer flow can be implemented in any groundwater flow modeling technique, including the Finite Difference Method as done in this thesis. Additionally, a field application of surface-groundwater flow modeling in the hummock and swale terrain of the Sheyenne National Grassland in North Dakota is presented. The purpose of the latter study is twofold: (1) assess the impact of future groundwater development on this sensitive ecosystem and (2) create accurate depth-to-groundwater maps to delineate areas where herbicides can be used without polluting groundwater. This work has practical implications for the protection of wetland ecosystems.