The use of Edge Notched Disc Beam (ENDB) sample has been proposed as a suitable geometry in performing fracture tests in different loading modes. The most important features of the ENDB samples include easy making, quick and easy sampling, simple testing, and the ability to examine a wide range of pure and combined loading modes. Using a wide range of fracture tests, a statistical model is proposed to predict the stress intensity factors of asphalt mixtures in terms of the pure torsion mode (mode III) loading in this study. To this end, the experiments were carried out at different temperature conditions (-5, -15 and -25 °C), different loading conditions (0.5, 1 and 5 mm/min), and on control and modified asphalt mixtures with different percentages of polyolefin-aramid fibers. The results showed that, with increasing the fiber content and loading rate, the fracture strength increased with average 25%, while an increase in fracture toughness due to lower temperature had an effect of less than 5%. Using the Response Surface Method (RSM), the prediction model of stress intensity coefficients of asphalt mixtures was presented in the pure torsion mode. The results of the proposed models had a good correlation with the results of the conducted fracture tests.