This article provides an analysis of the wire electrical discharge machining (EDM) process. The causes of wire vibration, bowing, and breakage are identified. The cross sectional configuration of an eroded wire is derived from basic physics under the assumption that the erosion rate is constant. This configuration is verified experimentally with further explanation as to why numerous experimental studies have yielded different configurations. A computational model has been developed that can evaluate the systematic effects that lead to wire breakage by determining the stress induced by wire erosion and the stress induced by the sparks during the operation of a wire-cutting EDM machine. This model is also capable of determining the extent of wire bowing and vibrations in these machines but only in the frontal direction. The model is supported by data from experiments performed on an AGIECUT 612 wire machine cutting a 10 mm high copper bar with a 0.15 mm brass wire to acquire wire breakage data. The nearly parabolic shape of the bowed wire agrees with the results of other authors making more restrictive assumptions.