The incorporation of various fibers into SBS-modified asphalt mixtures can markedly enhance their performance, offering a more economical approach than simply increasing the SBS content. This research investigated the effects of adding Basalt, Polyester, and Lignin fibers to a bitumen binder modified with 3% SBS and compared the results to a 7% SBS mixture without fibers. Laboratory evaluations, including indirect tensile strength and Dynamic Shear Rheometer (DSR) testing, were carried out to assess the mechanical properties of the mixtures. Additionally, finite element simulations based on the Burgers-Logit model were performed, along with microstrain analyses, to examine rutting and fatigue behavior, providing further context to the experimental findings. Results indicated that fiber-reinforced mixtures exhibited superior performance, with noticeable improvements in tensile strength and complex shear modulus. Among the fibers tested, Basalt fiber delivered the highest overall performance, surpassing the other types. Notably, the mixture containing Basalt fiber showed a 25% increase in rutting resistance and a 28% enhancement in fatigue damage resistance relative to the 7% SBS mixture.