 more which has been previously set according to a required specification. The present invention also provides a wire electric discharge machine in which electric discharge energy is supplied between a wire electrode and a workpiece by a machining electric power supply means so as to machine the workpiece in gas when the wire electrode and the workpiece are relatively traveled with each other by a positioning means, comprising a control means for controlling the positioning means so that a relative traveling speed of the wire electrode with the workpiece can be set at a variable speed not lower than a predetermined speed at which a short circuit between the electrodes can not continue for a predetermined period of time and more which has been previously set according to a required specification. The present invention also provides a wire electric discharge machine, further comprising a control means for controlling the variable relative traveling speed so that it can be increased in the case where the number of normal electric discharge pulses per unit time is large