The classical theory of elasticity (35) treats the material of a deformable body as a three-dimensional continuum in which internal stresses occur as the body is deformed by external forces acting over its surface. Although the internal stresses are caused by the displacement of atoms or molecules from an original state of equilibrium, the molecular character of the material is ignored. This means that every volume element within the material must contain enough molecules to guarantee that the thermal fluctuation of anyone molecule does not effect the local state of stress. Since biomembranes in general and red cell membranes in particular are only a few molecules thick, they can form a continuum only in the plane of the membrane. Thus, the methods of classical, three-dimensional continuum mechanics must be compressed into a two-dimensional world in which" stress resultants" or" tensions"(force per unit width of membrane surface) are defined on the surface of the membrane (8, 25, 48). Measurement of the surface stress resultants and the corresponding surface deformations permits the material properties of the membrane surface to be calculated (15, 16, 20). These surface properties represent a summation, over the thickness of the membrane, of the properties of the lamellar, molecular structures that form the membrane.