Non-circular holes are formed by electrochemical machining with an electrode that includes a hollow shank having a circular cross-section and a hollow tip section having a non-circular cross-section disposed on one end of the shank. The tip section is very small in length relative to the shank such that the shank comprises a large majority of the electrode's overall length. Because the majority of the electrode is circular in cross-section, it is relatively easy to straighten the electrode prior to a machining operation and to keep it straight during the operation, thereby overcoming problems experienced with full-length, non-circular electrodes. The circular shank also avoids electrolyte pressure imbalances eases the difficulty and high cost of manufacturing electrodes capable of forming non-circular holes.