Electricité de France (EDF) operates a large fleet of nuclear reactors and is responsible for demonstrating the safety of facilities, including concrete containment buildings (CCB), which are non-replaceable components. The leak-tightness of CCBs is assessed every 10 years during integrated leak-rate tests (IRLT). For double-wall containments, which have no metallic liners, the leak-tightness is strongly influenced by the degree of cracking of concrete and opening of the cracks, which mostly depends on (a) the prestress decrease due to the delayed strains of concrete and to a lesser extent due to relaxation of tendons steel, and (b) the saturation degree of the Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation concrete wall. Therefore, to optimize the maintenance programs on CCBs, it is important to predict the evolution of drying, creep and shrinkage strains of concrete to be able to correctly assess the pre-stress losses, and finally the air leak-tightness at a structural level during pressure tests or under accidental loadings. To improve our understanding and identify the best modelling practices on this issue, a large experimental program called VERCORS was launched in 2014. VERCORS is a 1/3 mock-up of a 1300 MWe nuclear reactor CCB. It has been widely instrumented, and its concrete thoroughly characterized. A specific attention has been paid to ensure it is consistent with real CBBs features in EDF's nuclear fleet. To complement its internal R&D efforts, EDF decided to associate external partners to this program. One of the means for this is the organization of benchmarks, where all teams are given data and information about the mock-up and are asked to quantitatively predict its behaviour. The present paper reports the organization and findings of the 2nd benchmark which was organized in 2018 and gathered several international teams around the same objective: improve the confidence in the modelling of structural behaviour as well as the leak-tightness of concrete in containment walls under pressure test loading. The benchmark has shown once again that predicting the mechanical and leakage behaviour of containment buildings is a difficult task. The benchmark also yielded interesting information about the possibility to use spatially reduced models to predict the mechanical behaviour and leakage and underlined the fact that more research must be done to better predict the localization of cracks and leakage. Some lessons have been learnt for the next benchmark: EDF will ask to clarify further the calibration methods, will give more data (including drying, creep and shrinkage at different temperatures and moisture measurements in the mock-up), and will help the participants using local leakage data by projecting the raw measurements on a regular grid, so that the local leakage models can be improved.