A variety of sustainability scenarios (e.g., IPCC's Emissions Scenarios) have been described toward a sustainable society. While many of them aim at solving climate change problems and they often assume various low-carbon technologies, the problem is that such scenarios hardly examine their feasibility from the viewpoint of resource depletion. In particular, copper is a critical base metal because introducing low-carbon technologies (e.g., electric vehicles and wind power generators) may induce copper consumption. To assess feasibility of existing sustainability scenarios, this paper proposes a method for estimating long-term copper demand based on those scenarios. Our method proposes an integrated model that evaluates world copper demand from two principal aspects of influencing copper consumption - (1) the building of social infrastructure and (2) new products that might disseminate in the future (e.g., electric vehicles and photovoltaic systems). A case analysis on a long-term energy scenario is carried out. Its results reveal that the cumulative copper consumptions in the world exceed the copper reserved in the earth by 2040. The increase in copper consumptions results mainly from world economic growth led by developing countries, while the dissemination of electric vehicles and photovoltaic systems has a minor impact on the consumption increase.