Determining the bituminous mixture’s resistance against elastic deformations is a critical parameter for designers. The presented standards have reviewed this index for semi-circular bending (SCB) geometry comprising 90-degree cracks; however, determining this index for SCB geometry containing inclined cracks can help the understanding of researchers in this field. By doing so, a total of five Hot Mix Asphalt (HMA) and five Warm Mix Asphalt (WMA) comprising different ratios of polyester fibers (PEF) and calcium lignosulfonate powder (CLSP) were constructed and tested. The results indicated that the HMA mixture containing 0.25 % PEF + 6 % CLSP had the best performance in terms of two indicators pre-peak fracture energy (GPf) as well as after-peak fracture energy (GAf) at temperatures of −18 °C and +25 °C and under modes I and II. Moreover, the WMA mixture containing 6 % calcium lignosulfonate was selected as the best mixture concerning these two indicators. Under Mode II and for the modified HMA mixture with both additives, an increase of 74 and 49 % GPf and 70 and 69 % GPf was obtained at temperatures of −18 and +25 °C, respectively. Also, an increase of 144 and 78 % GPf (23 and 11 % GAf) and 145 and 46 % GPf (93 and 26 % GAf) were obtained under mode I at temperatures of −18 and +25 °C, respectively. On the other hand, under mode II and for the WMA mixture modified with 6 % CLSP, an increase of 24 % GAf at −18 °C and a 14 % increase of GAf at +25 °C was obtained. Under mode I, an increase of 60 % GPf and 84 % GAf and an increase of 1 % GPf and 24 % GAf was achieved at −18 °C and +25 °C. Regarding TSI and TS indicators, the finding demonstrated that the HMA mixture comprising various ratios of additives had a lower resistance to elastic deformation than the additives-modified WMA mixes at −18 °C (under modes I and II); however, mixes reinforced with additives had a higher mechanical response in absorbing the load introduced in the elastic region (+25 °C). The finding demonstrated that the stiffness of a bituminous mixture comprising inclined cracks can be determined by SCB geometry.