This paper presents an advanced modeling approach which significantly improves predictions of reaction rates and critical data that engineers need to design effective pressure relief systems. Ideally, pressure relief systems are sized exactly for the reaction characteristics of the chemicals in the vessel. However, with many chemicals and chemical mixtures, reaction chemistry is difficult to characterize because the individual components interact in complex ways. Furthermore, the high cost and risk of full-scale reactivity experiments make test data scarce. Chemical engineers bridge this gap in part with small-scale tests and modeling computer codes such as the one developed by the Design Institute for Emergency Relief Systems (DIERS). The comprehensive approach developed in this paper provides a reliable design basis for difficult systems, including highly energetic and nonideal reactions, systems with continuing reactions in piping and containment vessels, and systems where homogeneous bubble collapse caused by rapid depressurization could cause a catastrophic vessel failure. We first examine possible mechanisms for catastrophic vessel failure and associated consequences. Next, we outline a detailed approach for emergency relief system design and reactivity testing.