Definition of parameters of stable mining structures is the key to cost-eff ective, stable, secure and environmentally friendly operation of all mining and processing complex. When designing of external dump of overburden, one of the most important things is the operative account of the effect of weak bases on stability of rock structures. The article provides a method for calculating stability of slopes in an analytical form for approval cylindrical surface collapse. This method is easily automated for computer calculations and allows us to solve a wide range of direct and inverse problems in the design of technological parameters of mining facilities. Finding the minimum safety factor is produced by selection of the least stable surface as a result of repeated calculations using a computer. To accelerate the search for the most probable collapse of the surface in the program is implemented, “the falling ball method”.