The Canadian used fuel container for the long‐term containment of spent nuclear fuel in a deep geological repository comprises a 3‐mm copper corrosion barrier applied directly to a strong carbon steel container. Although a final site for the Canadian deep geological repository has not yet been chosen, the site selection process has narrowed down to two candidate locations with unique groundwater chemistry, particularly with respect to salinity. Therefore, to ensure the long‐term integrity of the used fuel container, the effect of a range of groundwater chemistries on copper corrosion must be understood. The primary variables of interest are the influence of chloride concentration and the consequences of the interaction of hydrogen sulphide, naturally present in the groundwaters in very low concentrations, with the copper cladding. An additional aspect that has been investigated is the behaviour of copper in pure water. The anoxic corrosion of copper can be inferred by the very slow release of hydrogen gas. In this paper, new data are presented, which demonstrate an extremely sensitive approach to quantify the very limited hydrogen release at 75°C. Initially, corrosion rates under conditions approximating an anticipated Canadian deep geological repository were significantly less than 0.5 nm/year and they invariably declined over the course of several months/years. The presence of chloride or hydrogen sulphide was found, under specific conditions, to stimulate short‐term corrosion behaviour, which was consistent with anion‐assisted surface rearrangement, not bulk corrosion.