The electrical discharge machining process of a ceramic composite material consisting of alumina and titanium carbide has been modelled as an unsteady state mathematical model and solved by using Galerkin’s implicit finite element method. For several selected currents and powers the spark melted and sublimated the workpiece to form a crater which gradually expanded outwards. The size and shape of the crater anticipated by the computation were in good agreement with the scanning electron micrograph of the crater formed in an experiment. An increased electric current and duty factor would increase the material removal rate in expense of roughened surface and deteriorated mechanical properties.