Cap rock failure assessment, either tensile fracturing or shear slip reactivation of pre-existing fault, is a key issue for preventing CO2 leakage from deep aquifer reservoirs up to the surface. For an appropriate use in risk management, the uncertainties associated with such studies should be investigated. Nevertheless, uncertainty analysis requires multiple simulations and a direct use of conventional numerical approaches might be too computer time-consuming. An alternative is to use conventional analytical models, but their assumptions appear to be too conservative. An intermediate approach is then proposed based on the response surface methodology, consisting in estimating the effective stress state after CO2 injection as a linear combination of the most influential site properties based on a limited number of numerical simulations. The decision maker is provided with three levels of information: (1) the identification of the most important site properties; (2) an analytical model for a quick assessment of the maximal sustainable overpressure and (3) a simplified model to be used in a computationally intensive uncertainty analysis framework. This generic methodology is illustrated with the Paris basin case using a large scale hydromechanical model to assess caprock failure in the injector zone.