Placing a geomembrane liner in the core of a dam is an alternative construction technique to traditional clay core types. This study aims to assess the performance of such internal geomembrane sealing systems in an earthen dam. Two-dimensional (2D) numerical analysis was performed to evaluate leakage through defective seams within an earthen dam. Five possible applications of internal geomembrane systems were initially modeled to locate the zero-pressure lines in an earthen dam. Then, another application where the geomembrane is placed on the upstream face was modeled to compare the upstream and internal geomembrane systems. The results of this study show that use of a geomembrane system, either upstream or internal, significantly decreases the pore pressure at the downstream face of the earthen dam. In addition, limit equilibrium analysis was performed to evaluate the effects of leakage through defects in geomembranes on the dam stability. The stability analyses for the upstream and downstream slopes were performed for three loading conditions: (1) end of construction, (2) long-term, and (3) rapid drawdown. The frequencies and locations of defective seams had a significant impact on the factors of safety of the downstream slope. It is shown that, in the case of upstream geomembrane systems, the factor of safety for the downstream slope has the highest value when the geomembrane hole occurs at a relatively lower location. On the other hand, in the case of internal geomembrane systems, the highest factor of safety occurs when the geomembrane hole is at a higher location. Additionally, rapid drawdown simulations show that the upstream slope of an embankment dam must be flat enough to overcome the upstream stability issues when geomembranes are placed within embankment dams. This study not only showed the advantages of using a geomembrane in the core of a dam as an impervious lining system but also provided comparative information on the performance of internal and upstream geomembrane systems with respect to the stability in earthen dams.