The freshwater table is the upper boundary of the entire freshwater lens and is very important for understanding the formation of freshwater lenses and for managing fresh groundwater on islands. However, little attention has been given to the position of the freshwater table, as it is difficult to visually distinguish it from the unsaturated zone in physical models. Under the natural conditions, the process of rainfall infiltration into soils involves both pore-water flow and air flow in soil voids, and thus, the airflow induced by infiltration has implications for groundwater recharge and formation of freshwater lenses. Therefore, research on the precipitation-fed freshwater table in an oceanic island should consider the water-air two-phase flow induced by rainwater infiltration. This study focuses on simulating the steady-state position of the freshwater table using TOUGH2/EOS7, a model that considers liquid and gas two-phase flow and brine, water and air three-component in unsaturated-saturated porous media, and verifying it by comparing the numerical results with the analytical solutions. The numerical results delineated the entire geometry of island freshwater lenses that involve a freshwater table replenished by precipitation, which were then compared with the Dupuit-Ghyben-Herzberg (DGH) analytical solutions that ignore the outflow face and with Van der Veer's analytical solutions that consider the outflow face. Reasonable fits between the numerical results and the DGH analytical solutions were obtained, with the exception that the lens obtained by the DGH analytical model is smaller in size than that simulated by the numerical model for various cases; a better agreement was found between the results from the numerical model and Van der Veer's analytical solutions for the homogeneous island case. The agreements between the results from the proposed numerical model and the DGH and Van der Veer's analytical models verified the proposed numerical model. The numerical modeling method investigated here enhanced the numerical simulation techniques for studying groundwater movements and the interaction of freshwater and saltwater on oceanic islands and can provide a reference for modeling more complicated island groundwater patterns.