Alternative stress evaluation criteria suitable for Finite Element Analysis (FEA) proposed by Okamoto et al. [1] have been studied by the Committee on Three Dimensional Finite Element Stress Evaluation (C-TDF) in Japan. Thermal stress ratchet criteria in plastic FEA are now under consideration. Two criteria are proposed: evaluating variations in plastic strain increments and evaluating variations in the width of elastic core. To verify the validity of these criteria, calculations were performed for several typical models in C-TDF [2]. This paper shows the results of a simple cylinder model. Cyclic plastic analyses were performed applying sustained internal pressure and alternating linear temperature distribution through the wall. Analyses were performed with various load ranges to evaluate the precise ratchet limit and its behavior across the limit. Both pressure and thermal stress were given parameters. In the analyses, Elastic-Perfectly-Plastic (EPP) material was used and also strain hardening material for comparison. The ratchet limit in the Code [3] is based on Miller’s theoretical analysis [4] for a cylinder assuming a uni-axial stress state, whereas real vessels are in multi-axial stress state. By our calculations, we also examined the ratchet limit in real vessels. The results show that for the cylinder in a multi-axial stress state, the ratchet limit rises 1.2 times the ratchet limit by the Code. The evaluation results show that variations in equivalent plastic strain increments can be used for ratchet criterion and ratcheting can be assessed by confirming the presence of elastic core in the second cycle.