Coronal Mass Ejections (CMEs) are one of the most violent phenomena found on the Sun. One model to explain their occurrence is the flux rope ejection model where these magnetic structures firt form in the solar corona then are ejected to produce a CME. We run simulations coupling two models. The Global Non-Linear Force-Free Field (GNLFFF) evolution model to follow the quasi-static formation of a flux rope and MHD simulations for the production of a CME through the loss of equilibrium and ejection of this flux rope in presence of solar gravity and density stratification. Our realistic multi-beta simulations describe the CME following the flux rope ejection and highlight the decisive role played by the gravity stratification on the CME propagation speed.