Recently the rheological method is applied to the study of the mechanical characteristics of clay or clayey soil. It is because the time factor can not be ignored for the study of the relationship between stress and strain. The author have experimentally researched the distribution functions(τ) of stress relaxation of clay based on the model of linear visco-elastic body. The distribution functionФ(τ) can be shown as: E(t)=∫∞０Ф(τ)e-τ/t dt+E0 The experimental results are as follows: (1) The distribution functions are varied with given constant initial strain (ε0), and it means that the assumption of lineality is not proper. (2) The assumption of lineality is not proper but the distribution functionsФ (1nτ) show the difference of the yield phenomena between the state of dry of optimum and that of wet of optimum, (3) And it can also precisely express the ~mechanical phenomena in the range of plastisity.