Experimental investigations have been performed to understand the effects of prior loading on the creep and stress relaxation behavior of an amorphous polymer (polyphenylene oxide) and a semi-crystalline polymer (high density polyethylene) at room temperature. Of particular interest was the positioning of creep and relaxation tests on the unloading segment of stress-strain curves for tensile and compressive loading. The data was found to be quite unlike that obtained in typical tests performed on the loading segment; i.e., with no unloading history. Specifically, in relaxation tests, rather than registering a monotonic drop, the stress first increases then decreases. The rate of change of stress, therefore, is initially positive and then becomes negative. Similarly, in creep tests, the strain was found to decrease at first, and then began to increase. This has been labeled as rate-reversal in the context of relaxation and creep test data, and, furthermore, the test point has been found to influence the stress-time and strain-time data, respectively. In relaxation, for instance, at large strain values, the initial increase in stress is considerably smaller than the subsequent drop and the rate reversal occurs very rapidly. Conversely, at smaller strain values, the initial increase in stress dominates and the rate reversal may occur only after several hours. Analogous changes are observed during creep as tests are performed at lower stress values. Preliminary attempts at modeling the aforementioned creep and relaxation behavior have been made by modifying the existing formulation of the viscoplasticity theory based on overstress, which is a constitutive state-variable based model. A modified, single-element standard linear solid serves as a suitable descriptor of the model. Linking of two elements in series has shown some promise towards the modeling of the rate-reversal behavior. Experimental data and results of preliminary simulations are presented in this study.