Injection of CO2 in saline aquifers or oil reservoirs cause changes of pressure, temperature, saturation and concentrations that affect the state of stress in the host rock, resulting in porosity and permeability variations. It is therefore a coupled hydro-mechanical and chemical (HMC) problem. The fault reactivation problem considers that shear (with dilatancy), tension or compression of filling material may cause changes in hydraulic properties. Numerical simulation of multiphase and multicomponent flow of CO2 with mechanical coupling allows realistic modeling of fault reactivation. A finite element procedure is presented that models multiphase fluid flow in a deformable and chemically sensitive reservoir crossed by geological faults in a coupled and totally implicit manner. Whether the fault is activated or not is governed by the boundary conditions of the problem and by the modeling of the constitutive behavior of involved materials. Regarding the reservoir, special attention has been given to the phenomena that can take place in carbonate reservoirs when CO2 is injected causing dissolution and precipitation of minerals such as calcite and dolomite. This process may have a significant influence on the hydraulic and mechanical properties of the rock by way of cementation, degradation, volume change, porosity variations and modification of pore structure.