Based on the experimental observations, a cyclic nonlinear viscoelastic constitutive model was proposed to describe the uniaxial time-dependent ratcheting of polyetherimide (PEI) polymer under tensioncompression and tensiontension cyclic loading. The model was constructed by extending the nonlinear viscoelastic Schapery model (Schapery, Polym. Eng. Sci., 9, 295 (1969)). The extension emphasized the changes of parameter functions used in the original model, which enabled the model to describe the ratcheting of polymer material. Comparing the simulations with corresponding experimental results, the capability of the extended model to predict the uniaxial time-dependent ratcheting of PEI was verified. It is shown that the extended model can reasonably describe the uniaxial time-dependent ratcheting of the polymer under the tensioncompression and tensiontension cyclic loading with different peak-holdings, stress rates, and stress levels. POLYM. ENG. SCI., 52:18741881, 2012. (c) 2012 Society of Plastics Engineers