Determining if and when a vessel and/or piping component is going to fail under fire exposure and/or from cold temperature embrittlement is an important factor in consequence analysis and risk assessment. This article describes detailed methods for establishing the conditions for vessel/piping failure and whether the material of construction for vessels and piping is properly selected for fire exposure and/or cold depressuring/relief. Several case studies are used to illustrate important concepts dealing with how wall temperatures should be calculated for single and multiphase systems in order to establish if a vessel and/or a piping component is going to fail. (c) 2014 American Institute of Chemical Engineers Process Saf Prog 34: 64-71, 2015