A displacement discontinuity boundary element method is presented to explicitly model the microstructure of asphalt mixtures and to predict their tensile strength and fracture energy density. The loading response of three mixtures was simulated to assess the mechanics of fracture in the Superpave indirect tension test. The predicted tensile strength and fracture energy density of three samples were comparable with the test results for the samples. The predicted crack initiation and crack propagation patterns are consistent with observed cracking behavior. The results also imply that fracture in mixtures can be modeled effectively using a micromechanical approach that allows for crack growth both along aggregate surfaces and through the aggregates. Finally, the nonlinear MohrCoulomb type of failure envelope used to model the mastic appears to result in reasonable predictions. It can be concluded that the explicit fracture modeling with the displacement discontinuity boundary element method has the potential to evaluate the mechanics of fracture in asphalt mixtures.