This article describes the results of the experimental research on the heat-affected zone of the subsurface layers of eroded surface on medium-alloyed samples of steel EN X37CrMoV5-1 (W.-Nr. 1.2343) which occurs in die-sinking electrical discharge machining with Cu electrode. It assesses the direct effect and consequences of the heat-affected zone on the final quality of the machined surface. The aim of the experiments was to contribute to the knowledge database defining the influence of the main technological parameters of electrical discharge machining on the microhardness changes and the total depth of the heat-affected zone of the subsurface layers of experimental samples. The results of the experimental measurement were transformed into the mathematical models allowing simulation and prediction of the final quality of the machined surface after die-sinking electrical discharge machining tool steels with Cu electrode. The purpose of the mathematical models is to determine the optimal combination of process parameters and thereby achieve the desired quality of the products produced by this advanced technology.