CO2 storage in deep aquifers is considered as a potential technology to reduce the greenhouse effects of CO2. Practically, a large-volume (>1 Mt/year) of CO2 could be injected into a system that consists of a highly porous host aquifer covered by a low-permeability sealing caprock. High-rate injection could result in the abrupt build-up of fluid pressures, deforming the aquifer and compromising the integrity of the caprock. The interaction between the fluid pressure and the mechanical reaction of the host aquifer results in a complex coupled system. The understanding of these hydromechanical processes is crucial to secure the CO2 sequestration. In this keynote lecture we investigate numerically the hydromechanical effects induced by CO2 injection on aquifer stability and the related interactions with the caprock. The proposed numerical approach incorporates the main involved physical mechanisms including the physical properties of supercritical CO2. A conceptual deep aquifer is modelled to investigate the state of the stress and strain during the injection process. The simulation shows that significant geomechanical variations occur during the early period of injection, in which fluid pressures increase sharply. This overpressure decreases the effective stress, which induces a volumetric expansion around the injection well. Due to the increase in porosity and permeability through the hydromechanical coupling, the fluid flows more easily. As the injection continues, the stress path moves away from the failure line, and the geomaterial returns to its elastic state. This study offers a robust theoretical and numerical tool for the risk management and safety of carbon dioxide injection.