The influence of the volume fraction (V f ) of copper, plated at room temperature over a DyBa 2 Cu 3 O 7¹¤ -coated conductor, on the tensile strain tolerance and stress tolerance of critical current at 77 K was studied over a wide range of copper V f values. The copper plating exerts a tensile stress during cooling because copper has a higher coefficient of thermal expansion than the substrate conductor. Before application of tensile strain, the copper plated at room temperature yielded at 77 K when the copper V f was lower than a critical value, and was in an elastic state at 77 K when the copper V f was higher than the critical value. The strain tolerance of critical current increased with increasing copper V f due to an increase in thermally induced compressive strain in the substrate tape. The stress tolerance of critical current decreased with increasing copper V f because copper is softer than the substrate tape. These results, together with the trade-off between strain tolerance and stress tolerance (i.e., stress tolerance decreases with increasing strain tolerance), were analyzed by modeling. The results show that the restriction imposed by the trade-off, which limits the ability to simultaneously obtain a high strain tolerance and a high stress tolerance, can be relaxed by strengthening the copper.