The viscoelastic and viscoplastic behaviors of high density polyethylene (HDPE) under uniaxial monotonic and cyclic loading are modeled using the modified viscoplasticity theory based on overstress (VBO). The viscoelastic modeling capabilities of the modified VBO are investigated by simulating the behavior of semicrystalline HDPE under uniaxial compression tests at different strain rates. In addition, the effects of the modification (introducing the variable "C" into an elastic strain rate equation) on VBO that has been made to construct the change in the elastic stiffness while loading and unloading are investigated. During first loading and unloading, the modification in the elastic strain rate equation improves the unloading behavior. To investigate how the variable "C" that is introduced in the elastic strain rate equation evolves during reloading, the cyclic behavior of HDPE is modeled. For a complete viscoelastic and viscoplastic behavior the relaxation and creep behaviors of HDPE are simulated as well in addition to stress and strain rate dependency. The influences of the strain (stress) levels where the relaxation (creep) experiments are performed are investigated. The simulation results are compared with the experimental data obtained by Zhang and Moore (1997, Polym. Eng. Sci., 37, pp. 404-413). A good match between experimental and simulation results are observed.