Red cells have three main characteristics: specific shape--discoidal, deformability and aggregability. To give an explanation for his specific shape there are two ways: a) one, use hypothesis from mechanics, as: interfacial pressure, stress, deformability; b) the other way try to explain it by using data from molecular structure of biomembrane and cytoskeleton who are responsible of specific interactions between molecules. First direction was supported by many models, interesting but unrealized some of them because the theories from macroscopic mechanics wasn't well supported. The second direction, even more interesting then the first, was the subject of many studies but none of them gives a complete explanation for this particular shape of red cells. In present, there are many artificial data obtained experimental or in relation with pathological states. In our opinion, sustained also of literature data, the Helfrich's model is the most truth-like. After 1970, W. Helfrich tries to give an explanation of the particular shape of red cells, based on the curvature of elasticity and the grade of filled with hemoglobin. This model was proved also by experimental data, using "simplified red cells", and has also many others extensions. In the same direction are the studies of T.M. Fischer who describes a shape memory of human red blood cells, sustained experimental.