The evolution of the yield surface, as predicted by a polycrystal plasticity model of a face-centered cubic material, is studied. Grains in the model polycrystal are endowed with a classical hardening law, which accounts for interaction among the slip system through a hardening matrix. In the literature, the elements of the hardening matrix are assumed non-negative. In the present work, the effect of negative elements in the hardening matrix on the evolution of the yield function, particularly, during monotonic tensile and shear deformation, is systematically studied. In particular, it is shown that certain parametric values simulate a substantial kinematic hardening, similar to experimental observations. The greatest kinematic hardening is obtained when the latent hardening ratio of the reverse slip systems is taken to be −1.2. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.