In this a set of constitutive equation relevant to the analysis of thermo-elasto-plastic materials with phase transformation during quenching process was presented on the basis of continuum thermo-dynamic. In calculating the transient thermal stresses, temperature between coolant and specimen(SM45C) surface was determined from the heat transfer coefficient. A calculation was made for specimen with 40mm in diameter quenched in coolant from $820^{circ}C$ and the results are as follow. Stresses at starting point of transformation always show the maximum tensile value. Reverse of stresses takes place after completion of transformation of inner part at specimen.