The purpose of this dissertation is to present a formula for calculating the cohomology ring of a homogeneous flag bundles of a compact and connected Lie G group. To conclude the result, the equivalent cohomology is used, in particular, its more algebraic approach. This implies introducing G modules and their equivalent theory, which also involves introducing Weil algebra, Cartans model and characteristic homomorphism. The income statement is also strongly based on the algebraic properties of the maximal torus of G.