Supply Chains have to be designed and managed holding simultaneously into account many different performance measures. Moreover, modern Supply Chains have to ensure satisfying performances despite an increasing degree of complexity and market uncertainty as well as be capable to limit the negative impacts of disruptive events. A multi-criteria robustness evaluation framework is proposed to deal with these challenges. The proposed approach allows to separately assessing the impact of various performance measures specifying tailor loss functions, being able to deal with non-linearity and asymmetric impacts. Moreover, an original Robustness Index is defined, in order to provide reliable estimations even in the presence of outliers and integrating information about kurtosis and skewness in the robustness estimation. The proposed framework is applied to a fictive industrial case to demonstrate its utilization and show the kind of analysis that can be done on the basis of the obtained results. The approach, simply requiring the definition of some parameters and the description of the characteristics of the Supply Chain configurations to be evaluated, is meant to be easily used by practitioners.