The containment building (CB) is known as the third and last safety barrier to protect the environment from diffusion of radioactive products. In 2014, Électricité de France (EDF) launched the VERCORS project to improve the knowledge of leak-tightness in the CB under air pressure loading and aging effects. VERCORS consists in a 1/3 scaled containment mock-up representing a 1300 MWe CB of a typical French pressurized water reactor (PWR). This paper presents the results of a numerical methodology applied on VERCORS mock-up. The simulation includes THM analysis in gusset, prestressing phase and pressurization phase, and is conducted through a finite element code, Cast3M. Concrete is modeled through 3D elements while rebars and tendons are modeled by 1D elements. Moreover, the delayed strains including creep and shrinkage are especially considered. The instantaneous prestress losses, which result from friction; relaxation and pull-in at wedge, are taken into account. Regarding the long-term prestress loss due to the delayed strains, it is achieved by a kinematic relationship at interface of concrete-tendons. To describe cracks in concrete, an elastic damage model is used for the concrete elements, and the post-processing of leak-tightness is based on the internal variable of the damage model and a hydric analysis. The mechanical results reveal different damage zones on the CB, which are distributed at gusset, hatch and dome.