Ash and slag materials are removed from boiler rooms of CHP “Combined Heat and Power Plant” (Teploelektrotsentral’) by hydraulic transport and disposed in ash dumps. These are specially organized areas encircled by protective dams depending on the relief either along the entire perimeter or only in certain low-lying areas. The dams of hydraulic structures must provide stability to the whole structure against the following factors: shear; stability of slopes against sliding; filtration resistance of a dam body soils; reliable slope protection against possible failure due to atmospheric precipitation; as well as against wave action of water (within a settling pond); sufficient excess of dam crest over water level of a pond, etc. The study focuse on the design of ash and slag dump embankment (for storage of the ash and slag removed from the boiler rooms of Karaganda CHP by hydraulic transport). Ash dump design requires a broad range of problems to be solved. These include determination of location, design features and type of embankment, area of the basin and volume of the stored waste, strength of the embankment structures, etc. In order to assess the condition of the ash dump design, the stability of the facility embankment slopes for different combinations of loads, the conditions of possible watering of the dams, the presence of “geomembrane”, and pore pressure need to be analysed. A software program based on the finite element method allows simulation of ground (soil) conditions based on the strength and strain characteristics of the dam body filling soils and the base soils. Safety factors of the outer (downstream) slopes of hydraulic structures is determined taking into account the category and design of a structure, type of base (foundation), criticality of the design process stage, and other factors on the basis of conditions that ensure the prevention of the onset of limit states. The most critical and characteristic cross-sections across the perimeter of the ash dump embankment were selected for the computations, based on the analysis of the designed hydraulic structure base lithological composition. According to the computations performed, the outer slopes of the embankment at the paths of wells No. 373-19, No. 381-19, characteristic of almost the entire length of the embankment, are stable for different combinations of loads.