Ratcheting, which is the strain accumulation observed under the unsymmetrical stress controlled loading and non-proportional loadings, is modeled using the simplified viscoplasticity theory based on overstress (VBO). The influences of kinematic hardening laws on the uniaxial and multiaxial non-proportional ratcheting behavior of CS 1026 carbon steel have been investigated. The following kinematic hardening rules have been considered: the classical kinematic hardening rule, the kinematic hardening rules introduced by Armstrong-Frederick, Burlet-Cailletaud and the modified Burlet-Cailletaud. The investigated loading conditions include uniaxial stress controlled test with non-zero mean stress, and axial strain controlled cyclic test of thin-walled tubular specimen in the presence of constant pressure. Numerical results are compared with the experimental data obtained by Hassan and Kyriakides [Hassan T, Kyriakides S. Ratcheting in cyclic plasticity, part 1: uniaxial behavior. Int J Plast 1992;8:91-116] and Hassan et al. [Hassan T, Corona E, Kyriakides S. Ratcheting in cyclic plasticity, part 1: multiaxial behavior. Int J Plast 1992;8:117-146]. It is observed that all investigated kinematic hardening rules do not improve ratcheting behavior under multiaxial loading, but over-prediction still exists. (C) 2007 Elsevier Ltd. All rights reserved.