Polymer geosynthetic reinforcements exhibit obvious viscous behaviours depending on the loading strain rate. These behaviours can be accurately described using a nonlinear three-component constitutive model. After implementing this model into the finite element software ABAQUS, it can be widely used for the analysis of geosynthetic-reinforced soil problems. The algorithm for the numerical integration of this elasto-viscoplastic model is explained in detail. Simulations of both in-isolation geosynthetic reinforcement and geosynthetic-reinforced soil specimen are performed to analyse the viscous behaviours of polymer geosynthetics under complex loading histories. The corresponding user subroutines are provided in the supplementary data for potential readers.