The purpose of this study is to predict the stress of concrete for heating under constant strain. The free thermal expansion of concrete were measured for heating from 20℃ to 100℃. The stress relaxations were measured for five hours at the constant temperature of 20℃, 60℃, and 100℃. The initial stress levels of the stress relaxations were 1/6, 2/6, 3/6 and 4/6 of compressive strength. The concrete specimens were heated from 30℃ to 100℃, and the stress were measured under constant strain. The conclusion is the following ; For equal levels of initial stress, stress relaxation increases with temperature of concrete, within the limits of this experiment. As the initial stress level in concrete is increased, the stress relaxation also increases. The stress of concrete for heating under constant strain, could be predicted from the free thermal expansion and from stress relaxation.