The effect of thermal cycling on the state of stress in polymeric materials bonded to stiff elastic substrates was investigated using numerical techniques, including finite element methods. The work explored the relationship between a cyclic temperature environment, temperature-dependent viscoelastic behavior of polymers, and thermal stresses induced in a constrained system. Due to the complexity of developing a closed-form solution for a system with time, temperature, material properties, and boundary conditions all coupled, numerical techniques were used to acquire approximate solutions. Descriptions of attempted experimental verification are also included. The results of the numerical work indicate that residual stresses in an elastic-viscoelastic bimaterial system incrementally shift over time when subjected to thermal cycling. Tensile axial and peel stresses develop over a long period of time as a result of viscoelastic response to thermal stresses induced in the polymeric layer. The applied strain energy release rate at the crack tip of layered specimens is shown to similarly increase. The rate of change of the stress state is dependent upon the thermal cycling profile and the adhesive’s thermo-mechanical response. Discussion of the results focuses on the probability that the incrementing tensile residual stresses induced in an adhesive bond subjected by thermal cycling may lead to damage and debonding, thus reducing durability. / Master of Science