The Exploration Company is a French and German start-up that develops and operates Nyx, anorbital vehicle that also has a lunar version. This thesis focuses on the modeling and simulationof the o-design operation of the cryogenic engine of Nyx. The objectives of the thesis are tocreate a model on EcosimPro that can accurately model the steady state of the engine and itssubsystems and to use it to generate the operating o-design domain.First, a state of the art about the particularity of this study is performed. Indeed, the engineis using electrical pumps (e-pump) and is a LOX/methane engine, which is quite new for rocketengines. The state of the art enables to assess the feasibility of such an engine and to emphasizethe challenges associated with those new systems. The advantages of using a cycle with e-pumpswith regard to other classical cycles are described and their feasibility is conrmed. An exampleof such cyle is presented, the Rutherford engine, but using RP-1 as propellant. The problematicsassociated with methane such as the heat transfer deterioration or the pyrolisis are discussed, andthe injection role in combustion stability is discussed. It also introduces the simulation softwareEcosimPro and assesses its capability to model transient phases and steady states of a rocketengine.A rst model is created with components coming from the ESPSS library and is used to studythe behavior of the engine when throttling is performed. The heat transfer problem between thechamber and the regenerative cooling system is discussed and the correlations used in the modelto calculate the heat transfer coecients are described. The performance maps of the pumpsand the way they are implemented in ESPSS are presented and the model of the subsystemis validated. The model used in ESPSS to simulate valves is discussed and compared to thetheoretical model. The full 1D model is then used to create a simplied model using correlationsand a theoretical model of each subsystem in order to save computation time. The engineparameters are scattered in order to take into account discrepancies between the model and thereality and uncertainties in the manufacturing process, in the regulation or in the measurements.A high number of engines are simulated and the operating domains are generated for the point at100 % thrust. The domains show that the regulation is well performed and that the engine hasa high probability of operating near the nominal point and meeting the requirements in termsof performances. It also enables to show that the subsystems are going to be able to operatewithin the range dened by the design team.