Formulations and numerical simulations of shape memory process are essential issues in mechanical characterizations of shape memory polymers (SMPs). In this study, tensile stress and strain in the typical four-step thermal shape memory process are formulated basing on a Neo-Hookean hyper-viscoelastic constitutive equation that could consider the time-temperature effect, where the stress evolution equations that could consider the coupling of hyperelastic and viscous properties are derived and applied to calibrate the hyper-viscoelastic material parameters of an epoxy SMP. The numerical simulation method of shape memory process is established by coding the Arrhenius equation and utilizing the commonly used 3D Neo-Hookean hyper-viscoelastic model in ABAQUS. To verify the numerical method, finite element simulations are performed to predict the shape memory experiments with different strains in free and constrained recovery modes. As a result, the maximum relative deviation of 6.3% between the numerical predictions and the experimental results indicates the reasonability of the numerical method. (C) 2018 Elsevier Ltd. All rights reserved.