Abstract: The process and rules of the initial cracking due to thermal fatigue are studied considering the multi-linear kinematic hardening of material, with a simple sample as model analyzed by FEM. During the half cycle of warming the crack is closing and its two wall surfaces extrude each other because of thermal expansion. Then, the plastic compressive deformation comes into being when the compressive stress reaches the yield limit. During the half cycle of cooling, the sample tends to restore its original shape. However, because the plastic compressive deformation formed before cannot come back, the crack opens gradually. One of the necessary conditions of the initial cracking due to thermal fatigue is that the material on high temperature side has been deformed compressively and plastically, which is different from the cracking due to common fatigue.