A self-consistent reptation theory that accounts for chain-tube interactions, segment connectivity, chain-length breathing, segmental stretch, and constraint release is proposed. Simulation results are compared semiquantitatively to experimental observations in single-step strain hows. Since stochastic simulation techniques are used, no approximations, such as independent alignment or consistent averaging are needed to obtain results. The simulation results show excellent agreement : with experimental trends in sheer and normal stress relaxations, including the second normal stress difference, well into the nonlinear regime. For most of these experiments, the original Doi and Edwards theory, which incorporates independent alignment or consistent averaging, is not satisfactory. In the following companion paper, we show how the model is capable of describing double-step-strain flows for all stress components. Subsequent papers show excellent agreement fur the inception of steady shear flow, and steady shear flow.