Cyclic loading tests were conducted basically under completely reversed strain controlled conditions with a strain rate of 1.1×102104 and a strain amplitude of 0.1 at 25°C for polyethylene (PE), polypropylene (PP), polycarbonate (PC) and polyphenylen-ether (PPE). The experimental results show that stress-strain hysteresis loops of such solid polymers have a different shape than those of metallic materials. PE, PP and PC have a small acute angle between the tangents to the loading and unloading branches and PPE has a boomerang-like shape. The viscoplastic constitutive model based on overstress (VBO) has been shown to reproduce various experimental hysteresis loops of most metallic materials but the original model is not so flexible enough to represent these shapes of polymeric materials. This paper suggests a modification method, which enable the modeling of hysteresis loops with a cusp applying to simulate the cyclic motion behavior of PE in extensive experiments within the framework of the VBO model.