Abstract: Routine tri-axial CU shear test results indicate the stress-strain relationships of the unsaturated MaLan loess are softening with increasing strain.For practice,an exponential constitutive model with two parameters is derived in this paper.This model can not only describe the stress strain relationship well when the axial strain is less than 15%,but also clearly represent physical behavior by using few parameters that can be easily determined.The results also show that parameters change exponentially with the moisture content and confining pressure.