Traffic loading has been associated with different main distresses occurring in the pavements. Fatigue cracking and rutting can be considered as the main distresses occurring in the pavement structure. Studies conducted in the past have shown improved mechanical performance of asphalt rubber mixtures, but only few of these studies are inclined in investigating the long-term mechanistic performance and the cost-effectiveness of the addition of rubber into asphalt mixtures. A mechanistic analysis utilising 3D Move software package was performed to assess the long-term fatigue performance and rutting performance of two different mixtures, namely: conventional hot mixed asphalt (HMA) and asphalt rubber (AR). Two different pavement construction scenarios were investigated as a newly constructed pavement structure and a rehabilitated overlay. Each mixture was analysed for two different vehicle speeds and two different pavement thicknesses that totalled 16 different 3D Move mechanistic analysis scenarios (2 asphalt mixtures ×  2 construction scenarios ×  2 vehicle speeds ×  2 pavement thicknesses). The maximum tensile strain at the bottom of the asphalt layer for each scenario was utilised to establish a fatigue ratio that compared AR to the corresponding conventional HMA pavement sections. In addition, a cost-effectiveness analysis was carried out for the same 16 scenarios. Overall, the mechanistic analysis showed that the fatigue life of an AR was six times greater than that of conventional HMA layer for a new construction, and for the overlay, AR had 40 times more fatigue life than a conventional HMA. The rutting life was also increased with the use of asphalt rubber. In the case of cost-effectiveness analysis, AR exhibited four times lower cost per 1000 fatigue life cycles and three times lower cost per cycle of rutting when compared to a conventional HMA in a new construction. For an overlay scenario, AR exhibited 23 times lower cost per 1000 fatigue life cycles and around four times lower cost per cycle of rutting compared to a conventional HMA overlay.