The electrochemical machining using the numerically controlled motion of wire tool-electrode is studied theoretically. The Laplace equation for the electrical field potential and the equation of workpiece surface evolution are used as the mathematical model of the process. The developed scheme of computer modeling of machining involves the computation of distribution of current density over the workpiece surface using the boundary element method; the determination of new position of workpiece surface taking into account possible topological changes and the motion of tool-electrode along the prescribed trajectory. Various schemes of electrochemical micromachining using the tool electrodes with various cross-section shapes and various types of motions are analyzed. (C) 2015 Elsevier Ltd. All rights reserved.