The safety study of a CO2 storage site requires the evaluation of the sustainable injection pressure. The faults are generally considered as one of the potential leakage paths as a fault zone could be more permeable than the neighbouring rock matrix. The pressure build up in the reservoir due to the injection procedure changes the stress field within the reservoir and its surrounding rocks. The decrease of effective stress in the vicinity of a fault, due to this pore pressure increase, may lead to fault failure, increasing its permeability or even creating induced seismicity. The aim of this study is to carry out large-scale 2D coupled hydromechanical simulations of the fault behaviour during and after the injection and to study the sensibility of the fault response regarding to some parameters.