Abstract：On the basis of the fractional calculus operator theory，the stress-strain relation of soft soil under the condition of loading with constant strain rate is proposed. The analysis results show that stress–strain of soft soil performs exponent relation，which can be proved by large amounts of triaxial tests(under constant strain rate). It is found that the order of fractional calculus keeps constant to the same kind of soil and characterize soft or hard soil. The test results show that there is a linear relationship between confining pressures and initial tangent modulus. Compared with Duncan-Chang model that hypothesizes stress-strain relation is hyperbolic in response to similar shape of experimental curve，the stress-strain relation from the fractional calculus has rigorous theoretical background. The major innovation of our researches is that the soil is considered as the matter whose behaviors are intermediate between that of the ideal solid and fluid，and it also may be the first known application of fractional calculus in soil stress-strain relation.
