In this paper we have studied, the Burstein-Moss shift (BMS) in quantum wires (QWs) and quantum dots (QDs) of ternary and quaternary types of optoelectronic materials on the basis of a newly formulated electron dispersion law which occurs as a result of heavy doping. It has been found, taking Hg1-xCdxTe and In1-xGaxAsyP1-y lattice matched to InP as examples, that the BMS increases with increasing electron concentration and decreases with increasing film thickness in oscillatory manners for both types of quantum confinements, although the variations are totally band structure dependent. The numerical values of BMS is greatest in QDs and least in QWs together with the fact that the BMS in quaternary materials is greater than that of ternary compounds. In addition the theoretical analysis is a quantitative agreement with the experimental datas as given elsewhere.