Abstract: By using the digital stress path controlled trixial apparatus,eight tests were conducted on standard sands under special stress paths starting from an initial K0 stress condition.At small strains,the variation of the stress line of equal strain was depicted.A formula of the Young’s modulus along an arbitrary stress path and its direction was derived.Besides,the poison’s ratio was also studied.On this basis,a constitutive model of sands that could consider the effect of complex stress condition was established.This model was capable of reflecting the major behavior of sand at small strain,such as non-linearity,high stiffness and drastic change with strain.It could also simulate the variation of stiffness induced by stress paths direction that was not considered in the common models.