The reproducibility of stress relaxation behavior over a long period of time and the evaluability of “permanent strength”, which is the residual stress after infinite time, were verified using existing stress relaxation models. Stress relaxation tests were conducted on three different types of ECAPed industrial pure copper specimens, each with different stress relaxation behavior. Stress–relaxation time relationships were analyzed using three types of models： logarithmic and power–law models formulated theoretically, and an empirical exponential model. All of the three models are sufficient to reproduce the stress relaxation behavior, regardless of the relaxation amount and relaxation time, within the range of the experimental data. On the other hand, the permanent strength obtained from extrapolation of the experimental data is correlated with the plastic strain rate at which the stress–relaxation behavior stagnates. In this samples, it is necessary to obtain experimental data from ׄε_p=3×10^–10/s to ׄε_p=8×10^–12/s for the logarithmic and power–law models, and to ׄε_p=2.5×10^–9/s for the exponential model. Therefore, the exponential type is not significantly affected by differences in relaxation behavior, suggesting that it is a highly effective model that can evaluate the permanent strength more validly with shorter experimental data than other models.