The infinite long hollow cylinder was selected as the model for studying the thermal stress inside the vascular wall during the common cryopreservation process (i.e. cooling-holding at a certain temperature-warming-holding at a second temperature). Transient distributions of temperature and stress were obtained; and effects of cooling rates, warming rates, the holding temperatures on this two distributions were analyzed. Coupled with the experimental results of other researchers, our theoretical predictions indicated that the appearance of the axial compressive stress during the initial period of cooling process was not the governing role that may cause the circumferential crack of the inner and outer vascular wall. Instead, it was the axial tensile stress during the initial period of the warming process that may cause the cracks. Furthermore, the stress history in the multi-steps warming methods was studied. Contrary to the common opinion, the results revealed that the multi-steps method could not decrease the maximal stress while it can change the temperature range containing the maximal stress from low temperature stage to relatively high temperature stage. As the flexibility of the blood vessel was partially recovered in the relative high temperature stage, it can bear the maximal stress that it cannot bear when still left in the low temperature stage, and the intrinsic feature of multi-steps warming method was revealed by this study. This paper provides a theoretical supplement to the study of Pegg et al. (1997) and Buján et al. (2001) published in the journal of Cryobiology.