Abstract: The analytical expressions and approximation expansion in series of the coefficient of linear expansion versus a wide range of temperature for carbon steel and pressure vessel steels were deduced based on the continum mechanics,mechanical properties of metals and microscopic theory of solid physics. A concept and definition of transition temperature Tc of linear expansion coefficient was firstly proposed. when the temperature was lower than Tc, the linear expansion coefficient increased with the increace of temperature, When lower than Tc it decreased with the increase of temperature. From a view of atomic theory of solid physics, the relationship between elastic modulus and temperature was deduced including the crystal dislocation resulted from the plastic deformations induced by thermal activation energy at high temperatures. The universal function expression for elastic modulus vs temperature for carbon steel and pressure vessel steels was obtained. The computed results by the above-mentioned formula agreed well with the experimental data.