Better understanding the boil-off phenomenon is necessary to optimize the storage and transportation of cryogenic liquids, especially during space missions where the cryogenic tank is subjected to various stresses. Here, a numerical study of sloshing and boiling in LH2 tanks using direct numerical simulation is presented. A compressible formalism is retained to capture phase change and interface deformation in a confined two-phase environment. Our objective is to analyze the behavior of the boil off rate in a sloshed cryogenic tank. A significant increase of the boiling rate is observed compared to the static configuration with the same parameters.