A novel multi-relaxation-recovery (RR) test was proposed based on cyclic stages of stress relaxation and stress recovery. Three nonlinear visco-elastic models, that is, the standard model and two models with two dashpots connected either in parallel or in series, were examined for the analysis of the test results. Each model contains a time-dependent, viscous branch and a time-independent, quasi-static branch. The examination suggests that the standard model can determine the long-term, load-carrying performance of polyethylene (PE) and identify a transition point for the onset of plastic deformation in the crystalline phase, but the models with two dashpots connected either in parallel or in series are needed to provide a close simulation of the experimentally measured stress response in both relaxation and recovery stages of the RR test. In this work, the mechanical performance of two PEs was compared based on RR test results at room temperature. The RR tests were also conducted at elevated temperatures to explore the possibility of quantifying the activation energies for deformation of the dashpots at the relaxation stage. It was found the RR test has the advantage of separating the time-dependent and time-independent components of stiffness of the materials. The study concludes that the RR test can provide data for determining parameters in Eyring’s model in order to characterize the contribution of time-dependent and time-independent components of the stress response to PE’s deformation.