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This paper was carried out to reveal the influence of plated copper onto the substrate tape constituting of DyBa2Cu3O7-δ, MgO, Ag, and Hastelloy C-276 on the stress-strain behavior, and tensile strain and stress tolerance of critical current at 77 K. From the analysis of the stress-strain relation of the copper-plated tape at 77 K, it was shown that the copper plated at room temperature is yielded in tension at 77 K due to the higher coefficient of the thermal expansion of copper than that of the substrate tape. The plated copper gave compressive strain to the substrate tape and, hence, the superconducting layer at 77 K, due to which the strain tolerance of critical current was improved. The observed improvement of the strain tolerance with increasing volume fraction of plated copper was quantitatively described from the viewpoint of the stress balance at 77 K between the substrate tape and yielded copper. The tolerant strain increased, but the tolerant stress decreased with increasing copper volume fraction. Such a tradeoff correlation between the tolerant strain and stress was well described by modeling analysis.