The effects of triangular and rectangular discharge current waveforms on anode erosion in wire electric discharge machining is investigated based on heat transfer analysis of half-space subject to time and space-dependent heat flux. The thermal load on the anode is simulated by a hear flux that is calculated from time-dependent discharge channel radius and energy. Evolution of the melting front during discharge, the molten volume at the experimental result for qualitative verification of the analysis. It is demonstrated that the triangular current waveform is more efficient in eroding the anode than the rectangular one.