Ratcheting behavior or cyclic mean stress relaxation can have a significant effect on multiaxial fatigue lives when compared to proportional loads of similar range. The most important feature for ratcheting simulation in cyclic plasticity constitutive models is the nonlinear kinematic (NLK) hardening rule, which causes the translation of the yield surface during a plastic strain increment. A general nonlinear kinematic hardening model capable of simulating uniaxial ratcheting, multiaxial ratcheting, and mean stress relaxation (MSR) response is presented in this paper to capture these effects in incremental plasticity simulations. The uniaxial/multiaxial loading paths, including cyclic MSR, are simulated accordingly. Verification of the proposed model is achieved by comparing the predicted results with experimental measurements with 316L tubular specimens and the results from other NLK models.