Recently, structural design against a new type of thermal ratcheting under a null-primary-stress condition has been required. The representative case is the thermal ratcheting of a hollow cylinder caused by a traveling temperature distribution. In this paper, the mechanism of this ratcheting is proposed, and the evaluation method of ratcheting strain is shown based on this mechanism. The proposed evaluation method is basically based on the hoop-membrane stress due to the axial temperature distribution, and considers the influence of axial bending stress and traveling distance of temperature distribution. Predicted results by this method correspond to numerical results by FEM and can conservatively estimate the experimental results with several kinds of traveling distance, stress levels, and two types of temperature hold for types 316 and 316FR stainless steels. [S0094-9930(00)01102-1]