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The viscoplastic constitutive theory based on overstress had reproduced such deformation of the polymers successfully. In this study the overstress model is applied to analyze the creep behavior of polyethylene beams at 25℃ subjected to a linearly increasing moment which is subsequently held constant. The numerical experiments show the significant loading rate effects, illustrating that the stress distribution at the moment increase depends on the moment rate. Such rate effects disappear with time when stresses are redistributed and reach equilibrium stress curve. 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