We conducted theoretical simulations for exploring the overall physical properties of the pristine SrFBiS2 as well as its derivative alloys (Sr1− x BaxFBiS2 (x = 0, 0.25, 0.5, 0.75, 1)) resulting from BiS2 layers via the compositional effect of substituting strontium with barium. In this respect, we computed the electronic and optical characteristics of Sr1− xBaxFBiS2 systems within the concentration limits of x varying from 0 to 1. Based on full-potential linear augmented plane wave scheme, we determined the structural properties of the Sr1− xBaxFBiS2 alloys, and the lattice parameter was found to increase with the augmentation of Ba concentration, which in turn agrees well with the available experimental works. The electronic band structures and density of states of Sr1− xBaxFBiS2 (0 ≤ x ≤ 1) alloys were also examined. According to our calculations, the parent compound SrFBiS2 has a semiconducting behavior and its energy gap is about 0.8 eV. The electronic band structures illustrated that the substitution of the divalent Ba+2 element instead of Sr+2 produces a semiconducting behavior for all Sr1− xBaxFBiS2 (0 ≤ x ≤ 1) alloys. When substituting Ba+2 with Sr+2, the acquired optical features, such as the dielectric function, refractive index, reflectivity, absorption coefficient, energy loss functions, and optical conductivity for Sr1− xBaxFBiS2 (0 ≤ x ≤ 1) alloys also exhibited a semiconducting nature. It is easily noticed that the maximum absorption coefficient changes with the variation of Ba concentration. Furthermore, a superior birefringence occurs in the concerned Sr1− xBaxFBiS2 alloys when the composition variation undergoes from x = 0 to 1. Intriguingly, the optical spectra for both parent compounds SrFBiS2 and BaFBiS2 and their ultimate Sr1− xBaxFBiS2 alloys displayed a high anisotropy. The viable significant role of the spin-orbit coupling in deciding the electronic structures and optical characteristics is due to the presence of heavy bismuth atoms. All our results determined for Sr1− xBaxFBiS2 systems are compared with the existing theoretical and experimental reports.