This work proposes a methodology to compare energy and material supply risks (SRs) using energy system models (ESMs) with multi-objective optimization (MOO) to analyze possible trade-offs between them. Indeed, on the one hand, the transition to renewable energy technologies is decreasing the fossil fuel import dependency that many countries have been suffering until today; on the other hand, such technologies are much more mineral-intensive than fossil-based ones. They may therefore be affected by possible bottlenecks along the entire supply chain, from raw materials extraction and processing to components assembly. All these steps have been considered “critical” worldwide in an increasing number of analyses, and policymakers are starting to be concerned, promoting new devoted policies. In this regard, ESMs represent suitable tools to test their effectiveness, but some research gaps exist concerning critical raw materials (CRMs) and technology supply chain assessments. Despite the number of studies evaluating future material requirements increases, such studies are usually done ex-post starting from already available energy transition scenarios and only consider geological availability as a criticality issue. A few studies propose instead ex-post SR assessments, while to the authors’ knowledge, no endogenous analyses are present that include material criticality terms in the optimization, meaning that current global and regional energy scenarios are not affected by potential risks concerning CRMs supply chains. That makes this work among the first-of-a-kind assessments of energy and material SRs in a multi-objective energy system optimization. The proposed methodology involves the consistent definition of the just-mentioned SRs for a reference energy system (that is described in terms of technologies and commodities) as two separate objective functions to be used in a MOO, that include risk indicators both at commodity and technology level. The adopted material commodity SR is based on well-established criticality methodologies, while an energy commodity SR was consistently derived from literature. Then, for each technology included in the analyzed energy system, the commodity SRs are aggregated to calculate material and energy technology SR indicators, by using specific material and energy consumptions. The trade-offs between system material and energy SRs, costs, and CO2 emissions were studied through MOO optimization for a case study developed within the open-source TEMOA framework, providing insights about technology competitiveness in terms of energy security.