The Coulomb stress change has been widely employed to interpret mainshock-mainshock and mainshock-aftershock triggering as well as interactions amongst earthquake faults and volcanoes. This quantitative index is computed based on the Coulomb failure criterion and is a function of fault parameters including the source and receiver fault geometries, the friction coefficient on the receiver fault, and Skempton's coefficient of the host rock. Thus, for the robust determination of the Coulomb stress change, the sensitivity of the Coulomb stress change to these model parameters should be thoroughly assessed. However, notwithstanding numerous case studies, almost no systematic investigation of the sensitivity of the Coulomb stress change has been performed. Here we present an error estimator for the Coulomb stress change and then quantitatively investigate the sensitivity of the Coulomb stress change to the fault model parameters for the 2008 M w 7.9 Wenchuan earthquake. Our results indicate that for this case the Coulomb stress change is the most sensitive to the uncertainty in the dip angle of the receiver fault, while the influences of the uncertainties in the slip model of the source fault, the strike, and rake angles of the receiver fault, and the friction and Skempton's coefficients cannot be neglected. Accordingly, it is crucial to perform a realistic estimate of the uncertainty in the Coulomb stress change. By performing such calculation, future Coulomb stress analyses such as the stress triggering of earthquake sequence and the likelihoods of potential earthquakes could be based on more robust Coulomb stress change maps.