The present study provides a set of numerical tools for modeling the geomechanical aspects related to the safety of geological CO2 storage, namely, caprock damage and fault reactivitation due to reservoir pressure rise. Large scale finite element models are used to describe the injection process. The change of the effective stress field is investigated. Different cracking mechanisms are considered to examine the caprock integrity for high injection rates and different initial in situ stress conditions. Last, a special hydromechanical joint element is presented to model the response of the faults / fractures affected by the pressure build-up in the reservoir.