This paper presents a numerical modeling mechanism using a burger model to formulate a representation function that can be used to characterize relaxing properties and thermal cracking of asphalt mixtures. The objective of the paper is to (1) present a Burger Model Based Representation (BMBR) function and validate its feasibility and application using an asphalt paving project, and (2) advance characterizations of asphalt mixtures for future research work. The representation function presented in the paper is structured with a Maxwell model connecting with a Kelvin element known as a Burger model. An asphalt paving project was used to validate the applicability of the BMBR function and compare its prediction with the generalized Maxwell model. Based on numerical modeling results, the BMBR function is capable of predicting thermal cracking properties of asphalt mixtures within a reasonable accuracy as compared with the results from the generalized Maxwell model.