There are a number of long-term scenarios toward envisioning a sustainable society, particularly a low-carbon society. While such scenarios often assume various low-carbon technologies with an aim to reduce greenhouse gas emissions, it is unclear whether the scenarios are feasible from the viewpoint of resource depletion. For example, copper is a critical base metal since introducing low-carbon technologies (e.g., electric vehicle and wind power generator) may induce copper consumption. This paper proposes a method for estimating long-term metal demand based on sustainability scenarios. Our method proposes an integrated model that evaluates world metal demand from two different perspectives - (1) economic development and (2) dissemination of new products, e.g., electric vehicles. As a case study, the feasibility of a long-term energy scenario is assessed from the viewpoint of copper depletion. Results illustrate that the cumulative copper consumption exceeds the copper reserved in the earth by around 2040. The increase in copper consumption results mainly from world economic growth led by developing countries, while the dissemination of electric vehicles has a minor impact on the consumption increase.