Angular cracks are one of the types of cracks in asphalt mixtures that can be created due to the location of coarse aggregates as well as the weakness of the soft asphalt matrix (SAM). In this study, pure mode I was modeled to simulate the fracture behavior of hot mix asphalt (HMA) mixture containing angular cracks using the extended finite element method (XFEM). To improve HMA performance, calcium lignosulfonates (CL) additive and polyester fiber (PE), which were both environmentally and economically justifiable, were used. Numerical and experimental results showed that the proposed samples in both pure mode I (angular crack) and pure mode II (vertical crack) were able to model the fracture behavior of HMA; therefore, it can be used as suitable samples to study the pure mode crack deformation of HMA at low and intermediate temperatures. Also, the presence of coarse aggregate in the ligament section of the samples turned out to be an important factor in increasing fracture energy, fracture toughness, and reducing brittleness.