This paper presents a study carried out on reinforced concrete brick-filled composite beams. In reinforced concrete beams, less stressed concrete near neutral axis can be replaced by some light weight material like bricks to reduce the weight of the structure and also achieve the economy. Brick replacement zone is obtained with the help of stress block, used for limit state design of RC beams. Method of initial functions is used for the analysis of reinforced concrete brick filled composite beams. The method of initial function (MIF) is an analytical method of elasticity theory. Moreover, by saving concrete we save cement which also reduces the green house gases emissions. In this way sustainability can be achieved.