Asphalt mixture, an important part of roadway construction, is a type of typical viscoelastic materials. Temperature, speed and time of applied load etc. have obvious effects on asphalt mixture's mechanical property. It is necessary to research the material's constitutive relationship. Especially, there is an increasing need for the use of numerical methods in road design. In this study, several basic viscoelastic theories-small strain theory, Burgers model and Generalized Maxwell model are introduced. It is worth mentioning that some methods are illustrated about how to apply experimental data to finite element software. Ultimately, the study is aimed at providing numerical simulation that attempts to increase the prediction accuracy of stress in asphaltic pavement for more reliable pavement design.