Asphalt concrete pavements are inherently graded viscoelastic structures. Oxidative aging of asphalt binder and temperature cycling due to climatic conditions are the major cause of such graded non-homogeneity. Current pavement analysis and simulation procedures either ignore or use a layered approach to account for non-homogeneities. For instance, the recently developed Mechanistic-Empirical Design Guide (MEPDG) , which was recently approved by the American Association of State Highway and Transportation Officials (AASHTO), employs a layered analysis approach to simulate the effects of material aging gradients through the depth of the pavement as a function of pavement age. In the current work, a graded viscoelastic model has been implemented within a numerical framework for the simulation of asphalt pavement responses under various loading conditions. A functionally graded generalized Maxwell model has been used in the development of a constitutive model for asphalt concrete to account for aging and temperature induced property gradients. The associated finite element implementation of the constitutive model incorporates the generalized iso-parametric formulation (GIF) proposed by Kim and Paulino , which leads to the graded viscoelastic elements proposed in this work. A solution, based on the correspondence principle, has been implemented in conjunction with the collocation method, which leads to an efficient inverse numerical transform procedure. This work is the first of a two-part paper and focuses on the development, implementation and verification of the aforementioned analysis approach for functionally graded viscoelastic systems. The follow-up paper focuses on the application of this approach.