In this article, a typical and representative kinematic hardening soil model is first studied to investigate its capabilities to reproduce soil responses under principal stress rotations (PSR). It is found that the model is capable of reproducing the non-coaxiality very well. It can qualitatively capture the trends of responses of different stress and strain components, without the capability to quantitatively reproduce these responses. Its prediction of volumetric responses is the poorest and can give wrong results in many cases. The underlying reasons for these capabilities and defects are analyzed in detail. The model is subsequently modified to better take into account the PSR influences. An additional new flow rule and plastic modulus for the PSR are developed. One important feature of the model is that it is developed in the general stress space with six stress variables. Therefore, it can take into account multiple PSRs at different directions. Another feature is that it retains the linear stress rate–strain rate relationship, which facilitates its numerical implementations. In addition, the universal characteristic of the theory makes it equally applicable to other kinematic hardening models. Copyright © 2012 John Wiley & Sons, Ltd.