Generally, analytical consideration on the behaviour of metallic structures during quenching process, and analysis on the thermal stress and deformation after heat treatment are very important in presumption of crack and distorsion of quenched material. In this study a set of constitute equations relevant to the analysis of thermo elasto-viscoplastic materials with strain hysteresis during quenching process way presented on the basis of contimuum thermo-dynamics mechanics. The thermal stresses were numerically calculated by finite element technique of weighted residual method and the principle of virtual work. In the calculation process, the temperature depandency of physical and mechaniclal properties of the material in consideration. On the distribution of elasto-viscoplastic thermal stresses according to radial direction, axial and tangential stress are tensile stress(50㎫, 1.5㎬ and 300㎫) in surface and compressive stress(-1.2㎬, -1.14㎬ and -750㎫) in the inner part on the other hand, radial stress is tensile stress(900㎫) in area of analysis. According to axial direction, tangential stress gradients are average 60㎫/㎜ on the whole. The reversion of stress takes place at 11.5 to 16.8㎜ from the center in area of analysing.