Electrical discharge machining (EDM) is a promising non-traditional machining process, which is quite well investigated in relation to the formation of the plasma channel and the formation of single erosional craters. However, the influence of geometrical and energetic heterogeneities of electrodes on the formation of the workpiece shape and surface finish is insufficiently investigated.  In this work the analysis of the influence of geometric and energetic heterogeneities of the surfaces of the electrodes on the discharge and its location, the shape and size of the erosion craters is performed.  Theoretical studies based on multidischarge numerical simulation of electrical discharge machining, which includes a cyclical execution of the following steps [1]: 1) modeling of thermal processes for a single discharge; 2) modeling of the workpiece material removal and crater formation; 3) determining of the location of the subsequent discharge, are carried out.  For the simulation of thermal processes the equation of transient heat conduction in a medium with variable physical-chemical properties was used. Thus the workpiece material removal was replaced by an anisotropic material with low heat capacity, which allowed to eliminate the necessity of changing the computational domain when this material was removed. The boundary of the region filled with an anisotropic material was determined by solution of ordinary differential equation, which eliminates the possibility of repeated removal or deposition of material at any point on the workpiece surface during multidischarge EDM.  The location of the first pulse was set in the middle of the workpiece surface. The determination of the location of the next discharge taking into account the energy heterogeneity of the treated surface, was carried out on the basis of the analysis of the electric field in the interelectrode gap. The position of the next discharge was determined by the location of the point at which the modulus of the intensity of electric field has the greatest value.  The experimental investigation on the distribution of discharges over the workpiece surface at the initial stage of EDM was performed. The emergence of the phenomenon of "nesting" craters in the zones of maximum energy disposition (bulges, zones of differential surface and temperature) was shown. The process of how these zones are distributed over the entire workpiece surface was shown.