Abstract: The mechanism of the initialization of the cracks in the artery wall during cryopreservation was explored by using numerical simulation.A model based on the enthalpy theory was solved by using the finite difference method ,and a simulation program was used to predict the transient thermal field and thermal stress field across the artery wall.The effects of cooling rates, warming rates, holding temperatures on these two fields were analyzed.Coupled with the experimental results of other researchers,the authors,theoretical predictions indicated that the appearance of the axial compressive stress during the initial period of the cooling process was not the governing factor that may cause the circumferential crack in 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-step warming methods was studied.Contrary to the common opinion, the results revealed that the multi-step method could not decrease the maximal stress while it could shift the temperature range containing the maximal stress from low temperature stage to a relatively high temperature stage.As the flexibility of the blood vessel was partially recovered in the relative high temperature stage, it could bear the maximal stress,while this could not be done if still left in the low temperature stage.The intrinsic feature of the multi-step warming method was revealed by this study.