The strength in thermal stress cycling is one of the most complicated in the strength of material at high temperature, as the authors pointed out in the previous report. The study on such strength is important from fundamental and also practical point of view. Practically the structure members subjected to load at elevated temperature are not in a steady condition but in unsteady condition, as for stress and temperature, especially, variation of thermal stress is the most severe in the unsteady conditions. On the other hand, in recent years, attention has been placed on such an aspect of the fatigue problem that failure results from comparatively small cycles of severe stresses where strain amplitude of every cycle is the independent variable which destines the life. Also, attention has been given to the problem of influence of temperature variation on fatigue life. These attentions are focused on the problem of thermal stress cycling.The authors have been interested in the problem regarding the meaning of strain amplitude in thermal cycling test and in the study of the relationship between strength in thermal cycling and the fundamental strength at elevated temperature, such as static tensile strength, strength in strain-cycling, strength of creep rupture and others. The study on such relationship is practically important to make predictions as to test data under thermal cycling from the informations of other fundamental tests.The test of thermal cycling descrived above is that of completely reversed thermal stress cycling. However, the test of pulsating tensile thermal stress cycling is also necessary in order to know the relationship between the strength in thermal cycling and that of creep rupture. This is necessary to obtain the information of strength of material subjected to both mechanical steady stress and cyclic thermal stresses, from a practical point of view. Therefore, in the present paper, a test of pulsating thermal stress cycling on AISI 304 type stainless steels is performed, using the same testing apparatus as in the case of conventional thermal cycling test, being remodelled in gripping device so as to apply specimen tensile thermal stress only, free from the compressive stress. The test results under pulsating tensile thermal stress cycling are discussed in comparison with those under fully reversed thermal stress cycling. Attention is also placed on the relationship between the strength in pulstaing tensile thermal stress cycling and that of static creep rupture.Following are conclusions from the present study:(1) Failure life for pulsating tensile thermal stress cycling is much smaller than in the case of fully reversed thermal stress cycling, that is, the failure life under completely reversed cycling is nearly two hundred times as much as that under pulsating cycling as for the basis of total strain amplitude.(2) The life for pulsating tensile thermal stress cycling is a little smaller than that estimated from the criterion regarding life of creep rupture of the material subjected to simultaneous periodic variation of temperature and applied stress (Eq. 4), that is, the estimated result is nearly three times as big as the experimental one. It would mainly be because of neglecting exact calculation on the increase of thermal stress amplitude expected in accordance with the number of cycles in the criterion. Thus, in such a case of prediction, the effect of increase of thermal stress amplitude on the rupture life must be taken into consideration