Results of the joint project by the Working Group of Inelastic Analysis, Committee on High Temperature Strength, Society of Materials Science, Japan, are summarized. The purpose of this project, consisting of two parts, is to find out an appropriate inelastic constitutive equation which can simulate the new thermal ratchetting of a cylinder subjected to a traveling axial temperature distribution. In the first part of this project, uniaxial strain and stress-controlled ratchetting behavior is simulated by plural constitutive equations in order to examine the ability to reproduce basic deformation behavior of 316FR stainless steel at room temperature and 650 degreesC. In the second part, inelastic analyses of the thermal ratchetting of a cylinder due to a traveling temperature distribution are performed. Experimental data of ten specimens made of SUS 316 and 316FR stainless steels are prepared for evaluating the following items: traveling distance, stress level and hold time at high temperature. A comparison between experiments and corresponding inelastic analyses using eight types of constitutive models is made, and the selection of the appropriate constitutive equation is discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.