The need to maintain and expand hydraulic structures is a major challenge for the coming energy transition, especially in Western countries. One technique already widespread allowing to meet these issues consists in the use of geomembranes to overcome problems of permeability or deterioration of traditional linings. A recent development is the use of these geomembranes in pressure tunnels and penstocks in hydroelectric schemes in the form of geomembrane systems to increase their productivity and durability. However, although a few application cases have already been identified, little is known about the behavior of these geomembrane systems when faced with the high pressure and velocity flow that takes place in these pressure waterways and therefore very few technical recommendations are available for the installation of these systems. An in-depth study of the dynamic behavior of geomembrane systems when subjected to pressurized flow is therefore necessary to better understand how these systems interact with the flow, and in particular under what conditions membrane vibrations, potentially dangerous to the integrity of the structure, are likely to occur. The aim of this work is to contribute to this broad study of the dynamic behavior of geomembranes in pressurized flows by building a numerical model to simulate this problem, and to present the various issues and difficulties involved in its construction. The report details particularly how to take into account the hyperelastic behavior of the geomembrane material, how to define a mesh and load configuration that enable the membrane to withstand the high sollicitations imposed, and how to model the influence of the flow on the geomembrane and vice versa using the system coupling. Some preliminary results from the tests carried out show the consequences of the choices made, and give an idea of the capabilities and limits of the model. Indeed, the model still has its limitations, since, as explained in detail in this report, its development has proved far more difficult than anticipated, and numerous problems have arisen which have had to be resolved.