inaccurate for the internal problems, i.e., for the dam (as well as adjacent regions of the same size as the boundary element); it is also difficult to take the diversity of properties of the dam materials into account; b) in FEM, it is necessary to determine the load vector for all points on the basis of theoretical dependences (for example, taking account of the density of the dam material) and it is impossible to determine them from the condition of equilibrium at the boundary in terms of the stress; the nonlinearity is taken into account from a previously determined stress-strain relationship at the deviator stage of loading by means of iterative processes (whose convergence has not been proven), and the need to increase the number of finite elements in order to obtain a more accurate solution of systems of linear equations leads to computational difficulties. In the present work, we propose a method of calculating the SSS of waste-storage dams that is free from these deficiencies. Like FEM, the method proposed is based on the variational principle of a minimum of the total potential energy (TPE), which is obtained in searching for a minimum of the Lagrangian energy functional