The increase and change in traffic loading in recent years has resulted in the introduction of a new range of high performance asphalt binders. These new binders known as modified asphalt binders, have a more complex behavior than traditional binders. A review of the current mathematical models shows that most of them suffer from different drawbacks that make them inadequate for their intended application. To describe the behavior of straight and modified binders in the thermorheologically simple linear viscoelastic region, two models are proposed. Models to characterize the absolute value of the complex shear modulus (|G*|) and the phase angle (d) were developed using the matching function approach and validated by an experimental program. The dynamic mechanical properties of two typical paving grade binders and three modified binders were tested at intermediate and high service temperatures. Short-term and long-term aging were simulated by the rolling thin film oven test and the pressure aging vessel test, respectively. A dynamic shear rheometer with parallel plate configuration was used to conduct the dynamic mechanical tests at frequencies between 0.06 to 188.5 rad/sec and temperatures ranging from 5 to 75°C. Prior to the frequency sweeps, strain sweeps were performed to establish the linear viscoelastic region. Results indicated a strong susceptibility to the defined strain at intermediate temperatures; however, strain susceptibility was less pronounced at high temperatures. Frequency sweeps were then conducted at a constant strain corresponding to greater than 95% of the initial complex shear modulus as established by AASHTO TP5 for straight asphalts. The Time-Temperature Superposition Principle was used to construct the master curves. The shift factors were determined based on the complex shear modulus master curves and verified for the phase angle, storage shear modulus and loss shear modulus. After construction of the master curves, non-linear regression was used to fit the proposed models to the experimental data. Comparison between the measured and predicted values indicated a good agreement for frequencies higher than 10⁵ rad/sec. The phase angle model was found to adequately describe unmodified binder with a small percentage of errors (less than 6%). On the other hand, the phase angle model was found unable to simulate the plateau region observed for polymer-modified binders. However, the error in this case was found to be relatively small (from zero to 10%). The ability of the models to estimate other viscoelastic functions, e.g. storage shear modulus (G'), loss shear modulus (G"), and relaxation spectrum (H(t)), was found to be adequate. / Master of Science