The review examines modern knowledge on the mechanisms of the early stages of plant cell elongation growth. Coleoptiles are used as a model object representing juvenile organs of cereal seedlings. Elongation growth is considered to be a protective morphophysiological stage of seedling development during underground germination. The molecular mechanisms of elongation growth include: changes in the properties of the cell wall, activation of proton pumps, as well as aquaporins of plasma membrane and tonoplast. Particular attention is paid to the hormonal system of regulation, including auxin and ethylene. Coleoptiles of rice, a semi-aquatic plant tolerant to oxygen deficiency, demonstrate that the mechanisms of elongation growth are changing intensively under submergence, but they completely ensure cell growth. There is also a redistribution of importance and abundance between phytohormones. The data presented in the review indicate the necessity to continue investigations on the mechanisms of elongation growth under normal and stress conditions.