This paper focuses on the progress in geomechanical modeling associated with carbon dioxide(CO_2)geological storage.The detailed review of some geomechanical aspects,including numerical methods,stress analysis,ground deformation,fault reactivation,induced seismicity and crack propagation,is presented.It is indicated that although all the processes involved are not fully understood,integration of all available data,such as ground survey,geological conditions,microseismicity and ground level deformation,has led to many new insights into the rock mechanical response to CO_2 injection.The review also shows that in geomechanical modeling,continuum modeling methods are predominant compared with discontinuum methods.It is recommended to develop continuum-discontinuum numerical methods since they are more convenient for geomechanical modeling of CO_2 geological storage,especially for fracture propagation simulation.The Mohr-Coulomb criterion is widely used in prediction of rock mass mechanical behavior.It would be better to use a criterion considering the effect of the intermediate principal stress on rock mechanical behavior,especially for the stability analysis of deeply seated rock engineering.Some challenges related to geomechanical modeling of CO_2 geological storage are also discussed. This paper focuses on the progress in geomechanical modeling associated with carbon dioxide (CO_2) geological storage. Detailed specification of some geomechanical aspects, including numerical methods, stress analysis, ground deformation, fault reactivation, induced seismicity and crack propagation, is presented. At is indicated that although all the processes involved are not fully understood, integration of all available data, such as ground survey, geological conditions, microseismicity and ground level deformation, has led to many new insights into the rock mechanical response to CO_2 injection. review also shows that in geomechanical modeling, continuum-discontinuum numerical methods since they are more convenient for geomechanical modeling of CO_2 geological storage, especially for fracture propagation simulation. It is Mohr-Coulomb criterion is widely used in prediction of rock mass mechanical behavior. It would be better to use a criterion considering the effect of the intermediate principal stress on rock mechanical behavior, especially for the stability analysis of deeply seated rock engineering. Some challenges related to geomechanical modeling of CO_2 geological storage are also discussed.