Crystals of the composition Sr2-xBaxBi3 (0 <= x <= 1.3) have been synthesized from the elements and were characterized by single-crystal and powder X-ray diffraction methods. The compounds crystallize for x = 0, 0.45, 0.86, 1.08, 1.28 in the structure type of the parent compound Sr2Bi3 with space group Pnna (No. 52) and Z = 4. Substitution of Sir by Ba leads to a site preference for Ba. The anionic Bi substructures in the pseudoternary system simultaneously distort under remarkable elongation of one distinct Bi-Bi contact. Magnetic measurements for samples with x = 0, 0.45 and 1.08 reveal superconducting transitions at low temperatures. Linear muffin-tin orbital band structure calculations of Sr2Bi3 show strong cation-anion interactions that greatly stabilize the structure. Besides showing characteristics of a typical metal, the band structure plot unveils the coinstantaneous occurrence of flat and steep bands around the Fermi level indicative for superconductivity.