Temperature distribution, transformation and residual stresses generated during the quenching process of carbon steel. It follows many difficulties in the analytical considerations on those quenching process because of the coupling effects on temperature and metallic structures. In this paper one of the basic study on the quenching stresses was carried out for the case of the round steel bar specimen(SM45C) with 40mm both in its diameter and length. The temperature distributions considering strain hysteresis were numerically calculated by finite element technique. In calculating the transient temperature field, the heat flux between water and rod surface was determined from the heat transfer coefficient. The gradient of temperature is almost same to geometric of specimen. At early stage of the quenching process, the abrupt temperature gradient has been shown in the surface of the specimen.