Evaluation of localized peak strains at stress concentration zones under transient thermal loading is essential for the determination of low cycle fatigue life of a number of pressure vessels like steam turbine components and reactor vessels. Finite element analysis is a powerful technique but there are some difficulties in using the method for inelastic analysis of large-sized components. Several investigators have proposed approximate methods to determine inelastic strains at notches and other stress concentration zones from elastically calculated stress distributions. The accuracy of three of these methods, namely the Neuber rule, the Molski-Glinka rule and GLOSS analysis under thermal loading for axisymmetric pressure vessel bodies was investigated. A parametric study with geometry and material parameters as variables was carried out for three sizes of spheres with nozzles for the determination of peak strains and stresses under transient thermal loading using thermoelastoplastic finite element analyses and also by approximate methods. The same analyses have also been carried out for a steam turbine valve body for the same thermal loading, which is normally encountered by the valve body under start-up conditions. It has been found that GLOSS analysis is more accurate and the use of approximate methods has been recommended, especially for preliminary analyses in the development of new components.