A concept for a kinematic hardening yield surface in stress space for Cordova Cream limestone (Austin Chalk) developed by Celle and Cheatham (1981) has been improved using Ziegler's modification of Prager's hardening rule (Ziegler, 1959). Data to date agree with the formulated concepts. It is shown how kinematic hardening can be used to approximate the yield surface for a wide range of stress states past the initial yield surface. The particular difficulty of identifying the yield surface under conditions of unloading or extension is noted. A yield condition and hardening rule which account for the strain induced anisotropy in Cordova Cream Limestone were developed. Although the actual yield surface appears to involve some change of size and shape, it is concluded that true kinematic hardening provides a basis for engineering calculations.