Abstract The nuclear Components Code ∗ ∗ Section III-1971 of the ASME Boiler and Pressure Vessel Code. requires a detailed stress analysis, including the stresses caused by the transient temperature gradient across the thickness of the pressure boundary. By Code dèfinition, this thermal stress is composed of a linear portion (causing secondary stresses) and a nonlinear portion (causing peak skin stress). Using the across-the-thickness thermal transient as a basis of definition, this article derives the general expression for the linear and nonlinear portions of the transient. This derivation may be directly incorporated for evaluation of linear and nonlinear thermal stresses by a minor modification to a standard transient analysis computer code.