Geomembrane systems have been used in dams and reservoirs as rehabilitation technology since several decades and are now used worldwide. They act as impervious layer to prevent and mitigate water leakage and damage to structures. They meet the needs of many challenges faced by aging dams by improving their performance and lifespan, enhancing their resilience and sustainability. More recently, their application was extended to pressure waterways and surge shafts. A Finite Element model is developed to investigate the dynamic behavior of a framed hyperelastic geomembrane specimen for enhanced application in pressure waterways accounting for the dynamic behavior of the geomembrane system and fluid-structure interactions in the frequency domain. The nonlinear constitutive behavior of the geomembrane is modeled by the Mooney-Rivlin equation. The effect of water is considered by the added mass approach for the modal characteristics of the geomembrane. The damping is included as Rayleigh damping. Results show that the modal characteristics of the geomembrane are strongly influenced by the material nonlinear constitutive behavior. The first natural frequencies of the hyperelastic geomembrane specimen are found at low frequencies in vacuum. The natural frequencies also strongly increase with the increase of pre-tension in vacuum. In the presence of water, the variation of the natural frequency with pre-tension is highly reduced. The increase in hydrostatic pressure tends to moderately increase the natural frequencies of the specimen. Finally, the damping ratio has almost no influence on the natural frequencies.