The electrical discharge machining (EDM) is based on the material removal as consequence of the erosive effect of the electrical discharges in pulse, occurring between the electrode - tool (that contributes to the macroscopic localization of the process), and the workpiece - electrode, if there is an equipment that provides the adequate conditions for the machining development. Nowadays, the electrical discharge machining is applied especially in order either to obtain surfaces in workpieces made of electroconductive materials which are difficult to be machined by the so-called classical machining methods, or to obtain complex surfaces which are difficult to be obtained by the above mentioned classical machining methods. The electrical discharges develop between the closest asperities placed on the electrode tool and the workpiece; as consequence of these electrical discharges, small volumes of the electrode tool and workpiece materials are affected by a rapid increase of the temperature. Because the local temperatures exceed the melting and even vaporizing temperatures, small quantities of the heated material could be removed. If in the case of the workpiece this material removal is just the objective of the machining, for the electrode tool the material removal means his wear. At the machining on the ram EDM machines, there are sometimes situations when electrodes tools have both massive and thin zones; it is expected that these zones be affected in different ways by the wear phenomenon. The thinner is the electrode tool, the more intense could be the its wear, due to the difficulties in the evacuation of the heat generated by the electrical discharge machining process. The paper presents some theoretical considerations concerning the evolution of the electrode tool wear when the electrode tool includes zones having different thicknesses. Some experimental researches were also developed to highlight the evolution of the electrode tool zone.