A tailings dam is a large embankment structure that is constructed to store the waste from the mining industry. Stability problems may occur in a tailings dam due to factors such as quick rate of raising, internal erosion and liquefaction. The failure of a tailings dam may cause loss of human life and environmental degradation. Tailings Dams must not only be stable during the time the tailings storage facility is in operation, but also long time after the mine is closed. In Sweden, the licensing authorities demand that the tailings dams should be stable up to the next glaciation age, which is interpreted to be 1000 years or more. This goal requires extensive knowledge in order to be able to design the tailings dams so that they can be stable for such a long time. At the Division of Mining and Geotechnical Engineering at Luleå University of Technology, research has been conducted on the stability of tailings dams, using the finite element method which is considered to be suitable for modelling the complex geometry and the material properties of tailings dams. A case study is presented which describes the application of the finite element method in evaluating the stability of a tailings dam.