Knowledge of the mechanical and thermodynamic behavior of straight run asphalt is desirable in view of its use as a binder for pavement applications. The different complex processes undergone by asphalt concrete mixtures such as healing, aging, etc. can be understood more clearly, if one has a better understanding of the constitutive behavior of asphalt. The need is pressing as the use of polymer-modified asphalt as a binder has increased in recent years. Most of the studies carried out on constitutive modeling of asphalt model pure asphalt either as a Newtonian fluid or as a linear viscoelastic fluid over a wide range of temperatures. The complexity related to the study of the constitutive behavior of asphalt is compounded by the fact that asphalt is a mixture of different chemical species some of which are amorphous and some of which are crystalline in nature. The relaxation mechanisms of asphalt are diverse with different relaxation mechanisms at different temperatures. In this study, we use a thermodynamic framework for the constitutive modeling of asphalt and we model asphalt as a material with multiple relaxation mechanisms. This framework recognizes the fact that materials like asphalt can exist in more than one natural configuration (for instance, stress free configuration). We use the experimental data available in the literature (Lethersich, W., 1942. The mechanical behaviour of bitumen. Journal of the Society of Chemical Industry 61, 101–108; Cheung, C.Y., Cebon, D., 1997. Experimental study of pute bitumens in tension, compression, and shear. Journal of Rheology 41 (1), 45–73) for asphalt from different sources and demonstrate the efficacy of the model.