Elasticity of living soft tissues is strongly nonlinear. Based on experimental results on rabbits’ mesentery, a theoretical framework is presented in which the elastic properties of soft tissues can be described. It is shown that the mathematical formulation works well also in reducing published data on the series element of the heart and striated muscles, and the skin. In simple elongation the tensile stress is nearly an exponential function of the strain in the lower stress range. Based on this fact, it is shown that although we are dealing with the finite deformation of highly nonlinear materials, the elastic property of soft tissues in tension can be expressed quite simply in most cases. It is necessary, however, to give up the usual practice of trying to characterize the elasticity of a tissue by a representative Young’s modulus, because this modulus varies over a very wide range, which is often zero at vanishing stress, and increases linearly as the stress increases, and therefore is meaningless unless the exact stress level is specified. New physical constants recommended are, the slope and curvature at the origin of the curve of dT/dλ vs. T, where T stands for tension and X stands for the extension ratio, and the tensile stress T*, (based on the original crosssectional area) at a specific value of the extension ratio λ*.