The ratio of shear/normal stress reflects the deformation and failure characteristics of the friction material. By analyzing the shear/normal stress ratio under the change of magnitudes and directions of principal stresses, a nonlinear elastic model of soils considering the direction of principal stress axis is proposed based on the hyperbolic relationship between the shear/normal stress ratio and shear strain component. Considering the initial shear modulus and the strength of soil are closely related to the loading history and direction of stress, a method is given to determine the parameters of the model, and then a stress-strain relationship in the form of component is obtained. The rationality of the model is validated through stress path controlled triaxial test, pure principal stress axis rotation test and shear test with fixed direction of major principal stress. Comparisons of the predictions with the experimental results show that the deformation characteristics of soils under complex stress paths can be well quantified by the proposed nonlinear elastic model.