This article deals with the design of earth dams (estimating filter strength, compressibility and permeability of soils, studing of the stress-strain state, etc.) The authors look through a new, not previously discussed task of reliability of groundwater dams in extreme conditions like an influence of new and additional loads in the form of intense deformation of elongation and the base curvature. The dependences that allow determining the permissible values of deformations of ground dams earth surface on undermined territories are presented. The proposed method allows calculating the required parameters of structural and technological protection activities. In addition, the solution of such problems as predicting the behavior of the dam and its degree of reliability for a given expected deformation from external influence is found. The reliability forecasting of conventional dams, without undermining, can also be made.