The machining of a metal part by placing it as the anode in an electrolytic cell is well known. In this thesis we study a mathematical model of the process that consists of Laplace equation for the electrodes, together with an equation based on Faraday's and Ohm's laws that relates the electric field at the anode surface and the dissolution rate of (he anode surface. In this work a quasi-steady model, based on the irrotationality of the electric field between the electrodes, has been used. This problem is called Electrochemical Machining Problem (ECM). Two algorithms are given to solve the ECM, the first ((Time step algorithm)) gives the shape of the boundary as a set of points. While the second one ((Direct step algorithm)) gives a function which described the shape of the boundary for anv time in some interval.