Abstract: A series of true triaxial tests were performed with loading in directions of three principal stresses respectively. The obvious anisotropy induced by stress state were discovered. Based on the test results, the characteristics of the stress-strain softness matrix of soils, which indicate the rules of the relationship of the strain components in different stress directions, are proposed. These rules can be used to check whether a soil constitutive model is reasonable and suitable. In accordance with these characteristics, a constitutive model, which is based on Duncan’s hyperbolic model but modified to reflect the anisotropy, was developed. In different stress directions, Young’s modulus and Poisson’s ratio are different. The parameters of this model can be determined using ordinary triaxial tests, which are just the same as those in the hyperbolic model. The model is an experiential but practical anisotropic model of soils.