Estimation thermal stress with respect to viscoelasticity is much difficult. It is rea1ly difficult to
obtainthe accuracy of a solution dueto complicatted behhaviour of viscoelasticity. It possesses
memory on the past history of loading and remarkably time-temperature dependent. Through a
hereditary integral form of stress-strain relation, it is convenient to solve the solurion if the
viscoelastic response is characterized by relaxation modulus function, which is experimentally
measured over a time range. The characteristic is represented by the exponential series in time. On
this basis the theremal effect upon viscoelastic material is expressed by time-temperature
superposition principle. In solving viscoelastic problems, at each time increment the solution must
be saved and used to generate new solutions, involving summation back to time origin. Therefore, it
requires large amount of computer storage memory and solving times. To counter the problem, a
technique introduced by J.L White was employed in minimizing the regenration of stiffness
matrices at each time increment. In this study, road bridge model with asphaltic concrete pavement
was chosen in estimating temperature distribution, thermal stresses and deformations developed in
the interior section. The numerical analysis was performed utilizing the finite element computer
program based on time-dependent thermal conduction and viscooelastic constitutive theory. Under
non-traffic loading the influence of temperature variations upon structural materials was discussed.